I neutrini solari e da supernova (parte 1)

Corso di Introduzione all’astrofisica Anno accademico 2018-2019

Alessandra Re

I neutrini solari e da supernova (parte 1)

Cos’e’ il neutrino? •  Introdotto da Pauli nel 1930 per spiegare lo spettro continuo

dei decadimenti β- e β+;

•  La particella cosi’ introdotta deve avere –  Carica 0 (perche’ la carica sia conservata nel decadimento); –  Massa piccola, al limite nulla;

•  Alcuni anni dopo (1934) E. Fermi elabora il quadro teorico che descrive le cosiddette “interazioni deboli”, delle quali il decadimento β e’ un esempio;

•  Successivamente, viene elaborato da Glashow-Salam-Weinberg il cosiddetto Modello Standard delle interazioni deboli che riunisce in un’unica teoria interazioni elettromagnetiche e deboli;

AZX ! A

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AZX ! A

Z�1 Y+ e+ + ⌫e<latexit sha1_base64="PxdwVEu1RuIShCps/ecTbGCleBM=">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</latexit><latexit sha1_base64="PxdwVEu1RuIShCps/ecTbGCleBM=">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</latexit><latexit sha1_base64="PxdwVEu1RuIShCps/ecTbGCleBM=">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</latexit><latexit sha1_base64="PxdwVEu1RuIShCps/ecTbGCleBM=">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</latexit>

Una particella elusiva…. •  Nell’ambito del Modello Standard delle interazioni deboli il

neutrino ha le seguenti caratteristiche:

–  Ha carica nulla; –  E’ un fermione (cioe’ ha spin=1/2); –  Puo’ essere di tre sapori diversi: elettronico, muonico e

tauonico (νe, νµ, ντ) che formano altrettanti doppietti con I rispettivi leptoni carichi (e±, µ±, τ±);

–  Ha massa nulla; –  Interagisce esclusivamente tramite interazioni deboli;

•  Quest’ultimo fatto rende il neutrino particolarmente difficile da rivelare, in quanto le interazioni deboli hanno sezioni d’urto estremamente piccole;

•  Il neutrino viene rivelato sperimentalmente solo negli anni ’50 dall’esperimento di Cowan e Reines;

Esperimento di Cowan-Reines •  Ha fornito la prima evidenza sperimentale dell’esistenza dei neutrini (1956); •  Si e’ svolto in una stanza sotterranea al di sotto del reattore di Savannah

River; •  Ha rivelato gli anti-neutrini del reattore (Φ ~ 4x1012 cm-2 sec-1) tramite la

reazione

Seguita dopo ~10 µsec dalla reazione

eν1γ

2γ

+e n

Scintillatore plastico

Scintillatore plastico

Tanica di acqua con Gd

•  Quando un anti-neutrino interagisce si verificano quindi due eventi in sequenza, separati da una distanza temporale precisa •  Questo permette una chiara identificazione del segnale e una sicura riduzione del fondo; •  Tecnica delle coincidenze ritardate usata comunemente nella fisica nucleare;

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n + Gd ! �s<latexit sha1_base64="l3YHhGoVcGtjZ8cYI0ytzIBCuVQ=">AAACDXicbZDLSgMxFIYzXmu9jbp0E6yCIJQZKeiy4EKXFewFOqWcSdM2NMkMSUYpQ1/Aja/ixoUibt27823MtLPQ1h8CH/85h5zzhzFn2njet7O0vLK6tl7YKG5ube/sunv7DR0litA6iXikWiFoypmkdcMMp61YURAhp81wdJXVm/dUaRbJOzOOaUfAQLI+I2Cs1XWPAwFmqEQq8Rm+7uFAscHQgFLRAw4GIAR09aTrlryyNxVeBD+HEspV67pfQS8iiaDSEA5at30vNp0UlGGE00kxSDSNgYxgQNsWJQiqO+n0mgk+sU4P9yNlnzR46v6eSEFoPRah7cx21/O1zPyv1k5M/7KTMhknhkoy+6ifcGwinEWDe0xRYvjYAhDF7K6YDEEBMTbAog3Bnz95ERrnZd/ybaVUreRxFNAhOkKnyEcXqIpuUA3VEUGP6Bm9ojfnyXlx3p2PWeuSk88coD9yPn8ABeSbfA==</latexit><latexit sha1_base64="l3YHhGoVcGtjZ8cYI0ytzIBCuVQ=">AAACDXicbZDLSgMxFIYzXmu9jbp0E6yCIJQZKeiy4EKXFewFOqWcSdM2NMkMSUYpQ1/Aja/ixoUibt27823MtLPQ1h8CH/85h5zzhzFn2njet7O0vLK6tl7YKG5ube/sunv7DR0litA6iXikWiFoypmkdcMMp61YURAhp81wdJXVm/dUaRbJOzOOaUfAQLI+I2Cs1XWPAwFmqEQq8Rm+7uFAscHQgFLRAw4GIAR09aTrlryyNxVeBD+HEspV67pfQS8iiaDSEA5at30vNp0UlGGE00kxSDSNgYxgQNsWJQiqO+n0mgk+sU4P9yNlnzR46v6eSEFoPRah7cx21/O1zPyv1k5M/7KTMhknhkoy+6ifcGwinEWDe0xRYvjYAhDF7K6YDEEBMTbAog3Bnz95ERrnZd/ybaVUreRxFNAhOkKnyEcXqIpuUA3VEUGP6Bm9ojfnyXlx3p2PWeuSk88coD9yPn8ABeSbfA==</latexit><latexit sha1_base64="l3YHhGoVcGtjZ8cYI0ytzIBCuVQ=">AAACDXicbZDLSgMxFIYzXmu9jbp0E6yCIJQZKeiy4EKXFewFOqWcSdM2NMkMSUYpQ1/Aja/ixoUibt27823MtLPQ1h8CH/85h5zzhzFn2njet7O0vLK6tl7YKG5ube/sunv7DR0litA6iXikWiFoypmkdcMMp61YURAhp81wdJXVm/dUaRbJOzOOaUfAQLI+I2Cs1XWPAwFmqEQq8Rm+7uFAscHQgFLRAw4GIAR09aTrlryyNxVeBD+HEspV67pfQS8iiaDSEA5at30vNp0UlGGE00kxSDSNgYxgQNsWJQiqO+n0mgk+sU4P9yNlnzR46v6eSEFoPRah7cx21/O1zPyv1k5M/7KTMhknhkoy+6ifcGwinEWDe0xRYvjYAhDF7K6YDEEBMTbAog3Bnz95ERrnZd/ybaVUreRxFNAhOkKnyEcXqIpuUA3VEUGP6Bm9ojfnyXlx3p2PWeuSk88coD9yPn8ABeSbfA==</latexit><latexit sha1_base64="l3YHhGoVcGtjZ8cYI0ytzIBCuVQ=">AAACDXicbZDLSgMxFIYzXmu9jbp0E6yCIJQZKeiy4EKXFewFOqWcSdM2NMkMSUYpQ1/Aja/ixoUibt27823MtLPQ1h8CH/85h5zzhzFn2njet7O0vLK6tl7YKG5ube/sunv7DR0litA6iXikWiFoypmkdcMMp61YURAhp81wdJXVm/dUaRbJOzOOaUfAQLI+I2Cs1XWPAwFmqEQq8Rm+7uFAscHQgFLRAw4GIAR09aTrlryyNxVeBD+HEspV67pfQS8iiaDSEA5at30vNp0UlGGE00kxSDSNgYxgQNsWJQiqO+n0mgk+sU4P9yNlnzR46v6eSEFoPRah7cx21/O1zPyv1k5M/7KTMhknhkoy+6ifcGwinEWDe0xRYvjYAhDF7K6YDEEBMTbAog3Bnz95ERrnZd/ybaVUreRxFNAhOkKnyEcXqIpuUA3VEUGP6Bm9ojfnyXlx3p2PWeuSk88coD9yPn8ABeSbfA==</latexit>

Elusivo = difficile da rivelare •  Il numero di interazioni (ovvero il numero di volte in cui il

neutrino viene “rivelato”) e’ pari a

•  Siccome σ e’ piccola ( ~10-38, 10-45 cm2 a seconda della reazione) per avere un numero di interazioni sufficiente e’ necessario che ntgt sia grande;

•  Per fare un paragone: le σ nucleari sono ~ 10-24 cm2 (1 barn)! •  SONO NECESSARI RIVELATORI CON GRANDI MASSE

(parliamo di masse da 1000 a 10000 tonnellate!)

N = � · � · ntgt<latexit sha1_base64="VLXM8UZ5fpakhR114DBid0WT9Y4=">AAACE3icbVDLSgMxFM3UV62vqks3wSKIizIjgm6EohtXUsE+oFNKJs1MQ5PMkNwRytB/cOOvuHGhiFs37vwb03YW2nogcHLOvSTnBIngBlz32yksLa+srhXXSxubW9s75d29polTTVmDxiLW7YAYJrhiDeAgWDvRjMhAsFYwvJ74rQemDY/VPYwS1pUkUjzklICVeuUTXxIYaJndXvr1Acc+7ceAfcMjSfKL6mUQwXjcK1fcqjsFXiReTiooR71X/vL7MU0lU0AFMabjuQl0M6KBU8HGJT81LCF0SCLWsVQRyUw3m2Ya4yOr9HEYa3sU4Kn6eyMj0piRDOzkJIGZ9ybif14nhfCim3GVpMAUnT0UpgJDjCcF4T7XjIIYWUKo5vavmA6IJhRsjSVbgjcfeZE0T6ue5XdnldpVXkcRHaBDdIw8dI5q6AbVUQNR9Iie0St6c56cF+fd+ZiNFpx8Zx/9gfP5AwgHnkE=</latexit><latexit sha1_base64="VLXM8UZ5fpakhR114DBid0WT9Y4=">AAACE3icbVDLSgMxFM3UV62vqks3wSKIizIjgm6EohtXUsE+oFNKJs1MQ5PMkNwRytB/cOOvuHGhiFs37vwb03YW2nogcHLOvSTnBIngBlz32yksLa+srhXXSxubW9s75d29polTTVmDxiLW7YAYJrhiDeAgWDvRjMhAsFYwvJ74rQemDY/VPYwS1pUkUjzklICVeuUTXxIYaJndXvr1Acc+7ceAfcMjSfKL6mUQwXjcK1fcqjsFXiReTiooR71X/vL7MU0lU0AFMabjuQl0M6KBU8HGJT81LCF0SCLWsVQRyUw3m2Ya4yOr9HEYa3sU4Kn6eyMj0piRDOzkJIGZ9ybif14nhfCim3GVpMAUnT0UpgJDjCcF4T7XjIIYWUKo5vavmA6IJhRsjSVbgjcfeZE0T6ue5XdnldpVXkcRHaBDdIw8dI5q6AbVUQNR9Iie0St6c56cF+fd+ZiNFpx8Zx/9gfP5AwgHnkE=</latexit><latexit sha1_base64="VLXM8UZ5fpakhR114DBid0WT9Y4=">AAACE3icbVDLSgMxFM3UV62vqks3wSKIizIjgm6EohtXUsE+oFNKJs1MQ5PMkNwRytB/cOOvuHGhiFs37vwb03YW2nogcHLOvSTnBIngBlz32yksLa+srhXXSxubW9s75d29polTTVmDxiLW7YAYJrhiDeAgWDvRjMhAsFYwvJ74rQemDY/VPYwS1pUkUjzklICVeuUTXxIYaJndXvr1Acc+7ceAfcMjSfKL6mUQwXjcK1fcqjsFXiReTiooR71X/vL7MU0lU0AFMabjuQl0M6KBU8HGJT81LCF0SCLWsVQRyUw3m2Ya4yOr9HEYa3sU4Kn6eyMj0piRDOzkJIGZ9ybif14nhfCim3GVpMAUnT0UpgJDjCcF4T7XjIIYWUKo5vavmA6IJhRsjSVbgjcfeZE0T6ue5XdnldpVXkcRHaBDdIw8dI5q6AbVUQNR9Iie0St6c56cF+fd+ZiNFpx8Zx/9gfP5AwgHnkE=</latexit><latexit sha1_base64="VLXM8UZ5fpakhR114DBid0WT9Y4=">AAACE3icbVDLSgMxFM3UV62vqks3wSKIizIjgm6EohtXUsE+oFNKJs1MQ5PMkNwRytB/cOOvuHGhiFs37vwb03YW2nogcHLOvSTnBIngBlz32yksLa+srhXXSxubW9s75d29polTTVmDxiLW7YAYJrhiDeAgWDvRjMhAsFYwvJ74rQemDY/VPYwS1pUkUjzklICVeuUTXxIYaJndXvr1Acc+7ceAfcMjSfKL6mUQwXjcK1fcqjsFXiReTiooR71X/vL7MU0lU0AFMabjuQl0M6KBU8HGJT81LCF0SCLWsVQRyUw3m2Ya4yOr9HEYa3sU4Kn6eyMj0piRDOzkJIGZ9ybif14nhfCim3GVpMAUnT0UpgJDjCcF4T7XjIIYWUKo5vavmA6IJhRsjSVbgjcfeZE0T6ue5XdnldpVXkcRHaBDdIw8dI5q6AbVUQNR9Iie0St6c56cF+fd+ZiNFpx8Zx/9gfP5AwgHnkE=</latexit>

Eventi/sec neutrini/cm2·sec

cm2 Numero bersagli


•  σ e’ ~10-42cm2

•  Φ ~ 1012 cm-2 sec-1

•  Ntgt? Dipende ovviamente dalla massa di H2O; •  Se MH2O ~ 50 litri ~ 50Kg = 5 x 104 g; •  Peso molecolare dell’acqua A= 18 à una mole di acqua = 18g; •  In 50 litri di H2O ci sono MH2O/A = 5 x 104 g/ 18 g ~ 3 x 103 moli; •  In 1 mole di sostanza c’e un numero di atomi/molecole = NA=6x1023; •  Ntgt = Nprotoni = 2 x 3 x 103 moli x 6x1023 = 3.6 x 1027


cm2 Numero bersagli

Che tasso di interazione aveva l’esperimento di Cowan-Reines?

Tasso di int = 1012 cm-2 sec-1x 10-42 cm2 x 3.6 x 1027= 3.6 x10-3 ev/sec=311 ev/giorno

Elusivo e’ bello! Paradossalmente proprio il fatto che il neutrino interagisca cosi’ debolmente con la materia e’ una caratteristica che lo rende piu’ interessante da un punto di vista astrofisico

Per es.: I neutrini prodotti nel centro del sole raggiungono la terra in soli 8 minuti di volo, fornendoci cosi’ informazioni sulle reazioni nucleari nel sole “in tempo reale”. I fotoni emessi allo stesso tempo nel centro del sole, impiegano circa 105 anni per raggiungere la terra!

•  Il fatto che i neutrini abbiano carica nulla e momento magnetico molto piccolo fa si che si propaghino in linea retta anche in presenza di forti campi magnetici;

Puntano alla sorgente che li ha prodotti e possono quindi fornire meglio di qualunque altra particella informazioni su dove nell’Universo avviene la produzione e accelerazione di particelle;

•  Mentre altre particelle di origine astrofisica rimangono intrappolate, o possono propagarsi solo lentamente, I neutrini sono in grado di sfuggire e raggiungere la terra “velocemente”;

Il problema del “fondo” •  Anche avendo a disposizione grandi masse di rivelatore il numero

di interazione che solitamente si riescono a ottenere e’ comunque basso (al massimo ~qualche decina di eventi al giorno);

•  Data l’esiguita’ del segnale di neutrino, e’ necessario evitare che venga sopraffatto da segnali spurii indotti da particelle di altra natura;

•  In altre parole bisogna fare in modo che il rapporto SEGNALE/RUMORE sia il piu’ alto possibile;

•  A seconda della reazione che si usa per rivelare i neutrini e della regione di energia dei neutrini che si vogliono rivelare, i tipo di “fondo” (“rumore”) piu’ fastidiosi possono essere diversi;

•  Strategie piu’ comuni (reminder): –  Il fondo indotto dai raggi cosmici (Flusso a livello del mare ~ 106 sec-1 · cm-2 e probabilita’ di interagire MOLTO piu’ alta dei neutrini perche’ sono in gran parte particelle cariche!);

–  Radioattivita’ naturale;

Laboratori sotterranei per schermare i raggi cosmici

Accurata selezione dei materiali in termini di radiopurezza

Neutrini solari

Neutrini solari •  Come fa il sole a produrre neutrini? •  Che energia hanno? •  Quanti sono? •  Come si possono rivelare?

•  Il sole e’ in vita da circa 4.5 miliardi di anni; •  Il Modello Solare Standard prevede che il sole si sostenti

grazie alle reazioni che producono He a partire da nuclei di H; •  La pressione generata da queste reazioni dall’interno verso

l’esterno controbilancia la pressione gravitazionale dall’esterno verso l’interno che porterebbe il sole a collassare in pochissimo tempo (equilibrio idrostatico);

•  La sequenza di reazioni che maggiormente contribuiscono e’ denominata “Ciclo protone-protone”;

•  La bassa sezione d’urto delle interazioni deboli che ne fanno parte e’ responsabile del fatto che il sole bruci lentamente e non esploda immediatamente dopo la formazione.

Luminosita’ del sole: LΘ= 3.92 · 1026 Watts = 2.4 · 1039 Mev/sec

La luminosita’ in neutrini e’ circa il 2% di quella in fotoni;

E⌫ 0.42MeV<latexit sha1_base64="njXAlEHMCu1n34SkQHrT4ODYROY=">AAACB3icdZDNSgMxFIUz/tb6V3UpSLAILqTMjENbdwUR3AgVbCt0SsmktxqayYxJRihDd258FTcuFHHrK7jzbcy0FVT0QODw3XvJvSeIOVPatj+smdm5+YXF3FJ+eWV1bb2wsdlUUSIpNGjEI3kZEAWcCWhopjlcxhJIGHBoBYPjrN66BalYJC70MIZOSK4E6zNKtEHdwo4fEn0tw/Skm/oiGfkcbrBd8lz/4Ayao26haJeOqmXXKxtq2xXHdTLjVrxDDzuGZCqiqerdwrvfi2gSgtCUE6Xajh3rTkqkZpTDKO8nCmJCB+QK2sYKEoLqpOM7RnjPkB7uR9I8ofGYfp9ISajUMAxMZ7a1+l3L4F+1dqL71U7KRJxoEHTyUT/hWEc4CwX3mASq+dAYQiUzu2J6TSSh2kSXNyF8XYr/N0235Bh/7hVrB9M4cmgb7aJ95KAKqqFTVEcNRNEdekBP6Nm6tx6tF+t10jpjTWe20A9Zb583iZjN</latexit><latexit sha1_base64="njXAlEHMCu1n34SkQHrT4ODYROY=">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</latexit><latexit sha1_base64="njXAlEHMCu1n34SkQHrT4ODYROY=">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</latexit><latexit sha1_base64="njXAlEHMCu1n34SkQHrT4ODYROY=">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</latexit>

E⌫ = 1.44MeV<latexit sha1_base64="38ts4R3potE/T/hWxRHm5yTvQ/s=">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</latexit><latexit sha1_base64="38ts4R3potE/T/hWxRHm5yTvQ/s=">AAACBXicdVDLSgMxFM34rPVVdamLYBFclDLTGdu6EAoiuBEq2Ad0SsmkaRuayQxJRijDbNz4K25cKOLWf3Dn35hpK6jogcDhnHPJvccLGZXKND+MhcWl5ZXVzFp2fWNzazu3s9uUQSQwaeCABaLtIUkY5aShqGKkHQqCfI+Rljc+T/3WLRGSBvxGTULS9dGQ0wHFSGmplztwfaRGwo8verHLowSeQavoOG7hijSTXi5vFm3LPLEdaBbLdrVSKWlyWrLLdknnzCnyYI56L/fu9gMc+YQrzJCUHcsMVTdGQlHMSJJ1I0lChMdoSDqacuQT2Y2nVyTwSCt9OAiEflzBqfp9Ika+lBPf08l0Z/nbS8W/vE6kBtVuTHkYKcLx7KNBxKAKYFoJ7FNBsGITTRAWVO8K8QgJhJUuLqtL+LoU/k+apaKl+bWTrxXmdWTAPjgEx8ACFVADl6AOGgCDO/AAnsCzcW88Gi/G6yy6YMxn9sAPGG+f+VeXgw==</latexit><latexit sha1_base64="38ts4R3potE/T/hWxRHm5yTvQ/s=">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</latexit><latexit sha1_base64="38ts4R3potE/T/hWxRHm5yTvQ/s=">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</latexit>

E⌫ = 0.863MeV<latexit sha1_base64="+DFsc+Lwc+1MXHI0d0S6ytkyT2c=">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</latexit><latexit sha1_base64="+DFsc+Lwc+1MXHI0d0S6ytkyT2c=">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</latexit><latexit sha1_base64="+DFsc+Lwc+1MXHI0d0S6ytkyT2c=">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</latexit><latexit sha1_base64="+DFsc+Lwc+1MXHI0d0S6ytkyT2c=">AAACBnicdZDLSgMxFIYz9VbrrepShGARXJSSVOllIRREcCNUsLXQKSWTpm1oJjMkGaEMXbnxVdy4UMStz+DOtzHTVlDRA4GP/z+HnPN7oeDaIPThpBYWl5ZX0quZtfWNza3s9k5TB5GirEEDEaiWRzQTXLKG4UawVqgY8T3BbrzRWeLf3DKleSCvzThkHZ8MJO9zSoyVutl91ydmqPz4vBu7MprAU4gKldKxm79kzUk3m0MFhBDGGCaAyyVkoVqtFHEF4sSylQPzqnez724voJHPpKGCaN3GKDSdmCjDqWCTjBtpFhI6IgPWtiiJz3Qnnp4xgYdW6cF+oOyTBk7V7xMx8bUe+57tTJbWv71E/MtrR6Zf6cRchpFhks4+6kcCmgAmmcAeV4waMbZAqOJ2V0iHRBFqbHIZG8LXpfB/aBYL2PLVSa6Wn8eRBnvgABwBDMqgBi5AHTQABXfgATyBZ+feeXRenNdZa8qZz+yCH+W8fQJed5ex</latexit>

E⌫ 15MeV<latexit sha1_base64="lqzY9hZPVeJYZg8RZXHWU4VCQyo=">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</latexit><latexit sha1_base64="lqzY9hZPVeJYZg8RZXHWU4VCQyo=">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</latexit><latexit sha1_base64="lqzY9hZPVeJYZg8RZXHWU4VCQyo=">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</latexit><latexit sha1_base64="lqzY9hZPVeJYZg8RZXHWU4VCQyo=">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</latexit>

E⌫ 18.8MeV<latexit sha1_base64="+3nr9AXJwQlJ6kfVQLB/4ODYFtU=">AAACCHicbZDLSsNAFIYnXmu9VV26cLAILkpJRLDLgghuhAr2Ak0Ik+lJO3QyiTMToYQs3fgqblwo4tZHcOfbOL0stPWHgY//nMOc8wcJZ0rb9re1tLyyurZe2Chubm3v7Jb29lsqTiWFJo15LDsBUcCZgKZmmkMnkUCigEM7GF6O6+0HkIrF4k6PEvAi0hcsZJRoY/mlIzcieiCj7MrPXJHm2OVwj51ateZWbqCV+6WyXbUnwovgzKCMZmr4pS+3F9M0AqEpJ0p1HTvRXkakZpRDXnRTBQmhQ9KHrkFBIlBeNjkkxyfG6eEwluYJjSfu74mMREqNosB0jtdW87Wx+V+tm+qw5mVMJKkGQacfhSnHOsbjVHCPSaCajwwQKpnZFdMBkYRqk13RhODMn7wIrbOqY/j2vFyvzOIooEN0jE6Rgy5QHV2jBmoiih7RM3pFb9aT9WK9Wx/T1iVrNnOA/sj6/AFGUZjA</latexit><latexit sha1_base64="+3nr9AXJwQlJ6kfVQLB/4ODYFtU=">AAACCHicbZDLSsNAFIYnXmu9VV26cLAILkpJRLDLgghuhAr2Ak0Ik+lJO3QyiTMToYQs3fgqblwo4tZHcOfbOL0stPWHgY//nMOc8wcJZ0rb9re1tLyyurZe2Chubm3v7Jb29lsqTiWFJo15LDsBUcCZgKZmmkMnkUCigEM7GF6O6+0HkIrF4k6PEvAi0hcsZJRoY/mlIzcieiCj7MrPXJHm2OVwj51ateZWbqCV+6WyXbUnwovgzKCMZmr4pS+3F9M0AqEpJ0p1HTvRXkakZpRDXnRTBQmhQ9KHrkFBIlBeNjkkxyfG6eEwluYJjSfu74mMREqNosB0jtdW87Wx+V+tm+qw5mVMJKkGQacfhSnHOsbjVHCPSaCajwwQKpnZFdMBkYRqk13RhODMn7wIrbOqY/j2vFyvzOIooEN0jE6Rgy5QHV2jBmoiih7RM3pFb9aT9WK9Wx/T1iVrNnOA/sj6/AFGUZjA</latexit><latexit sha1_base64="+3nr9AXJwQlJ6kfVQLB/4ODYFtU=">AAACCHicbZDLSsNAFIYnXmu9VV26cLAILkpJRLDLgghuhAr2Ak0Ik+lJO3QyiTMToYQs3fgqblwo4tZHcOfbOL0stPWHgY//nMOc8wcJZ0rb9re1tLyyurZe2Chubm3v7Jb29lsqTiWFJo15LDsBUcCZgKZmmkMnkUCigEM7GF6O6+0HkIrF4k6PEvAi0hcsZJRoY/mlIzcieiCj7MrPXJHm2OVwj51ateZWbqCV+6WyXbUnwovgzKCMZmr4pS+3F9M0AqEpJ0p1HTvRXkakZpRDXnRTBQmhQ9KHrkFBIlBeNjkkxyfG6eEwluYJjSfu74mMREqNosB0jtdW87Wx+V+tm+qw5mVMJKkGQacfhSnHOsbjVHCPSaCajwwQKpnZFdMBkYRqk13RhODMn7wIrbOqY/j2vFyvzOIooEN0jE6Rgy5QHV2jBmoiih7RM3pFb9aT9WK9Wx/T1iVrNnOA/sj6/AFGUZjA</latexit><latexit sha1_base64="+3nr9AXJwQlJ6kfVQLB/4ODYFtU=">AAACCHicbZDLSsNAFIYnXmu9VV26cLAILkpJRLDLgghuhAr2Ak0Ik+lJO3QyiTMToYQs3fgqblwo4tZHcOfbOL0stPWHgY//nMOc8wcJZ0rb9re1tLyyurZe2Chubm3v7Jb29lsqTiWFJo15LDsBUcCZgKZmmkMnkUCigEM7GF6O6+0HkIrF4k6PEvAi0hcsZJRoY/mlIzcieiCj7MrPXJHm2OVwj51ateZWbqCV+6WyXbUnwovgzKCMZmr4pS+3F9M0AqEpJ0p1HTvRXkakZpRDXnRTBQmhQ9KHrkFBIlBeNjkkxyfG6eEwluYJjSfu74mMREqNosB0jtdW87Wx+V+tm+qw5mVMJKkGQacfhSnHOsbjVHCPSaCajwwQKpnZFdMBkYRqk13RhODMn7wIrbOqY/j2vFyvzOIooEN0jE6Rgy5QHV2jBmoiih7RM3pFb9aT9WK9Wx/T1iVrNnOA/sj6/AFGUZjA</latexit>

La catena protone-protone

4p ! ↵+ 2e+ + 2⌫e<latexit sha1_base64="5/RVPytnhDcZapOGFPgaRBvkbUw=">AAACGHicdVBNSwMxFMz6bf2qevQSLIIg6KaItreiF48KtgrdWt6mr20wm12SrFKW/gwv/hUvHhTx6s1/Y7ZWUNGBkGHmPZKZMJHCWN9/9yYmp6ZnZufmCwuLS8srxdW1holTzbHOYxnryxAMSqGwboWVeJlohCiUeBFeH+f+xQ1qI2J1bgcJtiLoKdEVHKyT2sW9IALb11G2n9BAi17fgtbxLQ1AJn2gO7RM8WonvwOVtnHYLpb8Xd/3GWM0J+zwwHekWq2UWYWy3HIokTFO28W3oBPzNEJluQRjmsxPbCsDbQWXOCwEqcEE+DX0sOmogghNKxsFG9Itp3RoN9buKEtH6veNDCJjBlHoJvMY5reXi395zdR2K61MqCS1qPjnQ91UUhvTvCXaERq5lQNHgGvh/kp5HzRw67osuBK+ktL/SaO8yxw/2y/VjsZ1zJENskm2CSOHpEZOyCmpE07uyAN5Is/evffovXivn6MT3nhnnfyA9/YBioKeyg==</latexit><latexit sha1_base64="5/RVPytnhDcZapOGFPgaRBvkbUw=">AAACGHicdVBNSwMxFMz6bf2qevQSLIIg6KaItreiF48KtgrdWt6mr20wm12SrFKW/gwv/hUvHhTx6s1/Y7ZWUNGBkGHmPZKZMJHCWN9/9yYmp6ZnZufmCwuLS8srxdW1holTzbHOYxnryxAMSqGwboWVeJlohCiUeBFeH+f+xQ1qI2J1bgcJtiLoKdEVHKyT2sW9IALb11G2n9BAi17fgtbxLQ1AJn2gO7RM8WonvwOVtnHYLpb8Xd/3GWM0J+zwwHekWq2UWYWy3HIokTFO28W3oBPzNEJluQRjmsxPbCsDbQWXOCwEqcEE+DX0sOmogghNKxsFG9Itp3RoN9buKEtH6veNDCJjBlHoJvMY5reXi395zdR2K61MqCS1qPjnQ91UUhvTvCXaERq5lQNHgGvh/kp5HzRw67osuBK+ktL/SaO8yxw/2y/VjsZ1zJENskm2CSOHpEZOyCmpE07uyAN5Is/evffovXivn6MT3nhnnfyA9/YBioKeyg==</latexit><latexit sha1_base64="5/RVPytnhDcZapOGFPgaRBvkbUw=">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</latexit><latexit sha1_base64="5/RVPytnhDcZapOGFPgaRBvkbUw=">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</latexit>

E = 26MeV<latexit sha1_base64="ezf0KA3j1b/J3C1yffxRoYJ3HyI=">AAAB+3icdVDLSgMxFM3UV62vsS7dBIvgQsqkSB8LoSiCG6GCrYXOUDJp2oZmMkOSEcswv+LGhSJu/RF3/o2ZtoKKHggczrmXe3L8iDOlHefDyi0tr6yu5dcLG5tb2zv2brGjwlgS2iYhD2XXx4pyJmhbM81pN5IUBz6nt/7kPPNv76hULBQ3ehpRL8AjwYaMYG2kvl10A6zHMkguTitV9/iKdtK+XXLKjuMghGBGUK3qGNJo1CuoDlFmGZTAAq2+/e4OQhIHVGjCsVI95ETaS7DUjHCaFtxY0QiTCR7RnqECB1R5ySx7Cg+NMoDDUJonNJyp3zcSHCg1DXwzmSVVv71M/MvrxXpY9xImolhTQeaHhjGHOoRZEXDAJCWaTw3BRDKTFZIxlphoU1fBlPD1U/g/6VTKyPDrk1LzbFFHHuyDA3AEEKiBJrgELdAGBNyDB/AEnq3UerRerNf5aM5a7OyBH7DePgE+wJPs</latexit><latexit sha1_base64="ezf0KA3j1b/J3C1yffxRoYJ3HyI=">AAAB+3icdVDLSgMxFM3UV62vsS7dBIvgQsqkSB8LoSiCG6GCrYXOUDJp2oZmMkOSEcswv+LGhSJu/RF3/o2ZtoKKHggczrmXe3L8iDOlHefDyi0tr6yu5dcLG5tb2zv2brGjwlgS2iYhD2XXx4pyJmhbM81pN5IUBz6nt/7kPPNv76hULBQ3ehpRL8AjwYaMYG2kvl10A6zHMkguTitV9/iKdtK+XXLKjuMghGBGUK3qGNJo1CuoDlFmGZTAAq2+/e4OQhIHVGjCsVI95ETaS7DUjHCaFtxY0QiTCR7RnqECB1R5ySx7Cg+NMoDDUJonNJyp3zcSHCg1DXwzmSVVv71M/MvrxXpY9xImolhTQeaHhjGHOoRZEXDAJCWaTw3BRDKTFZIxlphoU1fBlPD1U/g/6VTKyPDrk1LzbFFHHuyDA3AEEKiBJrgELdAGBNyDB/AEnq3UerRerNf5aM5a7OyBH7DePgE+wJPs</latexit><latexit sha1_base64="ezf0KA3j1b/J3C1yffxRoYJ3HyI=">AAAB+3icdVDLSgMxFM3UV62vsS7dBIvgQsqkSB8LoSiCG6GCrYXOUDJp2oZmMkOSEcswv+LGhSJu/RF3/o2ZtoKKHggczrmXe3L8iDOlHefDyi0tr6yu5dcLG5tb2zv2brGjwlgS2iYhD2XXx4pyJmhbM81pN5IUBz6nt/7kPPNv76hULBQ3ehpRL8AjwYaMYG2kvl10A6zHMkguTitV9/iKdtK+XXLKjuMghGBGUK3qGNJo1CuoDlFmGZTAAq2+/e4OQhIHVGjCsVI95ETaS7DUjHCaFtxY0QiTCR7RnqECB1R5ySx7Cg+NMoDDUJonNJyp3zcSHCg1DXwzmSVVv71M/MvrxXpY9xImolhTQeaHhjGHOoRZEXDAJCWaTw3BRDKTFZIxlphoU1fBlPD1U/g/6VTKyPDrk1LzbFFHHuyDA3AEEKiBJrgELdAGBNyDB/AEnq3UerRerNf5aM5a7OyBH7DePgE+wJPs</latexit><latexit sha1_base64="ezf0KA3j1b/J3C1yffxRoYJ3HyI=">AAAB+3icdVDLSgMxFM3UV62vsS7dBIvgQsqkSB8LoSiCG6GCrYXOUDJp2oZmMkOSEcswv+LGhSJu/RF3/o2ZtoKKHggczrmXe3L8iDOlHefDyi0tr6yu5dcLG5tb2zv2brGjwlgS2iYhD2XXx4pyJmhbM81pN5IUBz6nt/7kPPNv76hULBQ3ehpRL8AjwYaMYG2kvl10A6zHMkguTitV9/iKdtK+XXLKjuMghGBGUK3qGNJo1CuoDlFmGZTAAq2+/e4OQhIHVGjCsVI95ETaS7DUjHCaFtxY0QiTCR7RnqECB1R5ySx7Cg+NMoDDUJonNJyp3zcSHCg1DXwzmSVVv71M/MvrxXpY9xImolhTQeaHhjGHOoRZEXDAJCWaTw3BRDKTFZIxlphoU1fBlPD1U/g/6VTKyPDrk1LzbFFHHuyDA3AEEKiBJrgELdAGBNyDB/AEnq3UerRerNf5aM5a7OyBH7DePgE+wJPs</latexit>

Previsioni del Modello Solare Standard • Il flusso totale di neutrini previsto sulla terra e’ Φν = 6.5· 1010 ν/sec ·cm2;

• Il Modello Solare Standard prevede il contributo delle singole sorgenti di neutrino;

• L’energia media dei neutrini solari e’ < 1MeV;

Previsioni del Modello Solare Standard

Sorgente Eν (MeV) Flusso (cm-2s-2)

pp 0 - 0.42 5.99x1010 (1±0.01)

pep 1.44 1.42x108 (1±0.01) hep 0 - 18.8 7.93x103 (1±0.15) 7Be 0.86(90%)-0.38(10

%) 4.48x109 (1±0.09) 8B 0 - 14.06 5.69x106 (1±0.13)

13N 0 - 1.2 3.07x108 (1±0.20) 15O 0 - 1.7 2.33x108 (1±0.23) 17F 0 - 1.7 5.84x106 (1±0.25)

Il flusso totale di neutrini previsto sulla terra e’ Φν = 6.5· 1010 ν/sec ·cm2;

• Il Modello Solare Standard prevede il contributo delle singole sorgenti di neutrino;

• L’energia media dei neutrini solari e’ < 1MeV;

Come si rivelano i neutrini solari? •  Le tecniche di rivelazione dei neutrini solari si possono

sostanzialmente dividere in due grandi categorie:

•  Esperimenti RADIOCHIMICI –  I neutrini inducono una reazione che produce dei nuclei di un

isotopo radioattivo caratteristico Y:

–  Periodicamente (~qualche mese), vengono raccolti con tecniche radiochimiche i nuclei radioattivi prodotti Y e vengono contati (sfruttando il fatto che sono radioattivi);

•  Esperimenti in TEMPO REALE –  I neutrini interagiscono producendo particelle secondarie che

vengono rivelate immediatamente; –  Con questa categoria di esperimenti e’ possibile non solo

contare i neutrini che hanno interagito, ma eventualmente misurarne l’energia e/o la direzione;

⌫e +AZX ! A

Z�1Y+ e�<latexit sha1_base64="9y9BrowvoR5871VqbEfBsWisK6w=">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</latexit><latexit sha1_base64="9y9BrowvoR5871VqbEfBsWisK6w=">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</latexit><latexit sha1_base64="9y9BrowvoR5871VqbEfBsWisK6w=">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</latexit><latexit sha1_base64="9y9BrowvoR5871VqbEfBsWisK6w=">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</latexit>

Esperimenti radiochimici: Homestake •  Homestake e’ stato costruito in

una miniera d’oro in South Dakota (1.5 Km di profondita’);

•  E’ cominciato all’inizio degli anni ‘60 e ha preso dati ininterrottamente per piu’ di 30 anni;

•  E’ essenzialmente una grossa tanica contenente

615 t di C2Cl4 (percloroetilene); •  Sfrutta la reazione:

•  Si noti che: •  La reazione ha una soglia, ovvero

un’energia minima che il νe deve avere per interagire → non tutti i neutrini solari vengono rivelati;

•  Per es. Non e’ sensibile ai neutrini del pp

•  La reazione e’ sensibile esclusivamente ai neutrini elettronici (ma teoricamente tutti i neutrini solari sono elettronici!)

⌫e +37Cl ! 37Ar + e�

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Eth = 810 keV<latexit sha1_base64="FaoGtjguLEFaqGrZvT4gdOFIflU=">AAACAXicdZDLSgMxFIYzXmu9Vd0IboJFcCElKWKnC6EggssK9gJtGTJp2oYmM0OSEcowbnwVNy4UcetbuPNtzLQVVPRA4OP/zyHn/H4kuDYIfTgLi0vLK6u5tfz6xubWdmFnt6nDWFHWoKEIVdsnmgkesIbhRrB2pBiRvmAtf3yR+a1bpjQPgxsziVhPkmHAB5wSYyWvsN+VxIyUTC69xIzScxej7smYNVOvUEQlhBDGGGaAK2fIQrXqlrELcWbZKoJ51b3Ce7cf0liywFBBtO5gFJleQpThVLA03401iwgdkyHrWAyIZLqXTC9I4ZFV+nAQKvsCA6fq94mESK0n0red2b76t5eJf3md2AzcXsKDKDYsoLOPBrGAJoRZHLDPFaNGTCwQqrjdFdIRUYQaG1rehvB1KfwfmuUStnx9Wqy58zhy4AAcgmOAQQXUwBWogwag4A48gCfw7Nw7j86L8zprXXDmM3vgRzlvnxpSlqA=</latexit><latexit sha1_base64="FaoGtjguLEFaqGrZvT4gdOFIflU=">AAACAXicdZDLSgMxFIYzXmu9Vd0IboJFcCElKWKnC6EggssK9gJtGTJp2oYmM0OSEcowbnwVNy4UcetbuPNtzLQVVPRA4OP/zyHn/H4kuDYIfTgLi0vLK6u5tfz6xubWdmFnt6nDWFHWoKEIVdsnmgkesIbhRrB2pBiRvmAtf3yR+a1bpjQPgxsziVhPkmHAB5wSYyWvsN+VxIyUTC69xIzScxej7smYNVOvUEQlhBDGGGaAK2fIQrXqlrELcWbZKoJ51b3Ce7cf0liywFBBtO5gFJleQpThVLA03401iwgdkyHrWAyIZLqXTC9I4ZFV+nAQKvsCA6fq94mESK0n0red2b76t5eJf3md2AzcXsKDKDYsoLOPBrGAJoRZHLDPFaNGTCwQqrjdFdIRUYQaG1rehvB1KfwfmuUStnx9Wqy58zhy4AAcgmOAQQXUwBWogwag4A48gCfw7Nw7j86L8zprXXDmM3vgRzlvnxpSlqA=</latexit><latexit sha1_base64="FaoGtjguLEFaqGrZvT4gdOFIflU=">AAACAXicdZDLSgMxFIYzXmu9Vd0IboJFcCElKWKnC6EggssK9gJtGTJp2oYmM0OSEcowbnwVNy4UcetbuPNtzLQVVPRA4OP/zyHn/H4kuDYIfTgLi0vLK6u5tfz6xubWdmFnt6nDWFHWoKEIVdsnmgkesIbhRrB2pBiRvmAtf3yR+a1bpjQPgxsziVhPkmHAB5wSYyWvsN+VxIyUTC69xIzScxej7smYNVOvUEQlhBDGGGaAK2fIQrXqlrELcWbZKoJ51b3Ce7cf0liywFBBtO5gFJleQpThVLA03401iwgdkyHrWAyIZLqXTC9I4ZFV+nAQKvsCA6fq94mESK0n0red2b76t5eJf3md2AzcXsKDKDYsoLOPBrGAJoRZHLDPFaNGTCwQqrjdFdIRUYQaG1rehvB1KfwfmuUStnx9Wqy58zhy4AAcgmOAQQXUwBWogwag4A48gCfw7Nw7j86L8zprXXDmM3vgRzlvnxpSlqA=</latexit><latexit sha1_base64="FaoGtjguLEFaqGrZvT4gdOFIflU=">AAACAXicdZDLSgMxFIYzXmu9Vd0IboJFcCElKWKnC6EggssK9gJtGTJp2oYmM0OSEcowbnwVNy4UcetbuPNtzLQVVPRA4OP/zyHn/H4kuDYIfTgLi0vLK6u5tfz6xubWdmFnt6nDWFHWoKEIVdsnmgkesIbhRrB2pBiRvmAtf3yR+a1bpjQPgxsziVhPkmHAB5wSYyWvsN+VxIyUTC69xIzScxej7smYNVOvUEQlhBDGGGaAK2fIQrXqlrELcWbZKoJ51b3Ce7cf0liywFBBtO5gFJleQpThVLA03401iwgdkyHrWAyIZLqXTC9I4ZFV+nAQKvsCA6fq94mESK0n0red2b76t5eJf3md2AzcXsKDKDYsoLOPBrGAJoRZHLDPFaNGTCwQqrjdFdIRUYQaG1rehvB1KfwfmuUStnx9Wqy58zhy4AAcgmOAQQXUwBWogwag4A48gCfw7Nw7j86L8zprXXDmM3vgRzlvnxpSlqA=</latexit>

� ⇡ 10�46 � 10�45 cm2<latexit sha1_base64="TczXH6yKOQOWbzZZP9lm71N4aPg=">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</latexit><latexit 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sha1_base64="TczXH6yKOQOWbzZZP9lm71N4aPg=">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</latexit>

νe

Vengono immessi in contatori proporzionali per vedere l’elettrone Auger prodotto quando decadono (τ=35 giorni)

L’esperimento e’ estremamente difficile: viene prodotto 1 atomo di 37Ar ogni due giorni!!

E’ importantissimo tenere sotto controllo le sistematiche (per es. efficienza di raccolta dell’Ar)

37Ar 37Ar 37Ar 37Ar

37Ar

37Ar

Homestake

Gli atomi di 37Ar vengono estratti una volta ogni 1-3 mesi facendo bubbolare He nella tanica

⌫e +37Cl ! 37Ar + e�

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I risultati di Homestake •  Homestake trova un flusso di

neutrini pari a 0.5 neutrini al giorno contro i ~1.5 neutrini al giorno previsti dal Modello Solare Standard;

•  Il fondo e’ principalmente dovuto a muoni cosmici residui che producono 37Ar interagendo con il Cl. Si stima che 1 nucleo di Ar su 6 sia dovuto a questo processo e non a interazione di neutrino;

•  Utilizzando le Solar Neutrino Units (SNU)

Φ = (2.6 ± 0.2) SNU •  La previsione

Φ = (7.9 ± 2.6) SNU


Cos’ e’ uno SNU (Solar Neutrino Unit)?

•  1 SNU = 10-36 Eventi/sec/tgt;


cm2 Numero bersagli

N

ntgt= � · �

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Esperimenti radiochimici: Gallex/GNO

•  Gallex e’ stato costruito nei Laboratori sotterranei del Gran Sasso in Abruzzo (~1.5Km di profondita’);

•  Ha preso dati dal 1990 al 2004; •  E’ essenzialmente una grossa

tanica contenente 30 t di Ga sotto forma di GaCl3-HCl (100 t);

•  Sfrutta la reazione:

•  Si noti che a differenza di Homestake, Gallex e’ in grado di rivelare almeno in parte i neutrini del pp

•  La reazione e’ sensibile esclusivamente ai neutrini elettronici (ma teoricamente tutti i neutrini solari sono elettronici!)

Eth = 233 keV<latexit sha1_base64="PuezdkceCZ4xk34E+zQxKT8l2+I=">AAACAXicdZDLSgMxFIYzXmu9jboR3ASL4ELKpBXbLoSCCC4r2At0hiGTZtrQzIUkI5Rh3Pgqblwo4ta3cOfbmGkrqOiBwMf/n0PO+b2YM6ks68NYWFxaXlktrBXXNza3ts2d3Y6MEkFom0Q8Ej0PS8pZSNuKKU57saA48DjteuOL3O/eUiFZFN6oSUydAA9D5jOClZZcc98OsBqJIL10UzXKzivVqn0ypp3MNUtW2bIshBDMAdXOLA2NRr2C6hDllq4SmFfLNd/tQUSSgIaKcCxlH1mxclIsFCOcZkU7kTTGZIyHtK8xxAGVTjq9IINHWhlAPxL6hQpO1e8TKQ6knASe7sz3lb+9XPzL6yfKrzspC+NE0ZDMPvITDlUE8zjggAlKFJ9owEQwvSskIywwUTq0og7h61L4P3QqZaT5+rTUbMzjKIADcAiOAQI10ARXoAXagIA78ACewLNxbzwaL8brrHXBmM/sgR9lvH0CGQuWoA==</latexit><latexit sha1_base64="PuezdkceCZ4xk34E+zQxKT8l2+I=">AAACAXicdZDLSgMxFIYzXmu9jboR3ASL4ELKpBXbLoSCCC4r2At0hiGTZtrQzIUkI5Rh3Pgqblwo4ta3cOfbmGkrqOiBwMf/n0PO+b2YM6ks68NYWFxaXlktrBXXNza3ts2d3Y6MEkFom0Q8Ej0PS8pZSNuKKU57saA48DjteuOL3O/eUiFZFN6oSUydAA9D5jOClZZcc98OsBqJIL10UzXKzivVqn0ypp3MNUtW2bIshBDMAdXOLA2NRr2C6hDllq4SmFfLNd/tQUSSgIaKcCxlH1mxclIsFCOcZkU7kTTGZIyHtK8xxAGVTjq9IINHWhlAPxL6hQpO1e8TKQ6knASe7sz3lb+9XPzL6yfKrzspC+NE0ZDMPvITDlUE8zjggAlKFJ9owEQwvSskIywwUTq0og7h61L4P3QqZaT5+rTUbMzjKIADcAiOAQI10ARXoAXagIA78ACewLNxbzwaL8brrHXBmM/sgR9lvH0CGQuWoA==</latexit><latexit sha1_base64="PuezdkceCZ4xk34E+zQxKT8l2+I=">AAACAXicdZDLSgMxFIYzXmu9jboR3ASL4ELKpBXbLoSCCC4r2At0hiGTZtrQzIUkI5Rh3Pgqblwo4ta3cOfbmGkrqOiBwMf/n0PO+b2YM6ks68NYWFxaXlktrBXXNza3ts2d3Y6MEkFom0Q8Ej0PS8pZSNuKKU57saA48DjteuOL3O/eUiFZFN6oSUydAA9D5jOClZZcc98OsBqJIL10UzXKzivVqn0ypp3MNUtW2bIshBDMAdXOLA2NRr2C6hDllq4SmFfLNd/tQUSSgIaKcCxlH1mxclIsFCOcZkU7kTTGZIyHtK8xxAGVTjq9IINHWhlAPxL6hQpO1e8TKQ6knASe7sz3lb+9XPzL6yfKrzspC+NE0ZDMPvITDlUE8zjggAlKFJ9owEQwvSskIywwUTq0og7h61L4P3QqZaT5+rTUbMzjKIADcAiOAQI10ARXoAXagIA78ACewLNxbzwaL8brrHXBmM/sgR9lvH0CGQuWoA==</latexit><latexit sha1_base64="PuezdkceCZ4xk34E+zQxKT8l2+I=">AAACAXicdZDLSgMxFIYzXmu9jboR3ASL4ELKpBXbLoSCCC4r2At0hiGTZtrQzIUkI5Rh3Pgqblwo4ta3cOfbmGkrqOiBwMf/n0PO+b2YM6ks68NYWFxaXlktrBXXNza3ts2d3Y6MEkFom0Q8Ej0PS8pZSNuKKU57saA48DjteuOL3O/eUiFZFN6oSUydAA9D5jOClZZcc98OsBqJIL10UzXKzivVqn0ypp3MNUtW2bIshBDMAdXOLA2NRr2C6hDllq4SmFfLNd/tQUSSgIaKcCxlH1mxclIsFCOcZkU7kTTGZIyHtK8xxAGVTjq9IINHWhlAPxL6hQpO1e8TKQ6knASe7sz3lb+9XPzL6yfKrzspC+NE0ZDMPvITDlUE8zjggAlKFJ9owEQwvSskIywwUTq0og7h61L4P3QqZaT5+rTUbMzjKIADcAiOAQI10ARXoAXagIA78ACewLNxbzwaL8brrHXBmM/sgR9lvH0CGQuWoA==</latexit>

⌫e +71 Ga !71 Ge + e�

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� ⇡ 10�45 � 10�44 cm2<latexit sha1_base64="JdOJ5VvYLlcthJ2qa/KzKL+6lNk=">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</latexit><latexit sha1_base64="JdOJ5VvYLlcthJ2qa/KzKL+6lNk=">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</latexit><latexit sha1_base64="JdOJ5VvYLlcthJ2qa/KzKL+6lNk=">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</latexit><latexit sha1_base64="JdOJ5VvYLlcthJ2qa/KzKL+6lNk=">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</latexit>

Vengono immessi in contatori proporzionali per vedere I raggi x prodotti quando decadono (τ=11 giorni)

L’esperimento e’ estremamente difficile: viene prodotto meno di 1 atomo di 71Ge al giorno!!

E’ importantissimo tenere sotto controllo le sistematiche (per es. efficienza di raccolta dell’Ge)

νe

Gli atomi di 71Ge (sottoforma di composto volatile GeCl4 ) vengono estratti una volta al mese facendo bubbolare N2 nella tanica

71Ge 71Ge 71Ge 71Ge 71Ge 71Ge

⌫e +71 Ga !71 Ge + e�

<latexit sha1_base64="/u/V37jc9V+WuU0NfD4tIaqmwLY=">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</latexit><latexit sha1_base64="/u/V37jc9V+WuU0NfD4tIaqmwLY=">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</latexit><latexit sha1_base64="/u/V37jc9V+WuU0NfD4tIaqmwLY=">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</latexit><latexit sha1_base64="/u/V37jc9V+WuU0NfD4tIaqmwLY=">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</latexit>

I risultati di Gallex/GNO

•  Gallex trova un flusso di meno di 1 neutrino al giorno ~ la meta’ del valore atteso;

•  Usando le Solar Neutrino Units Φ=69.3 ± 4.1(stat) ±3.6(sys)SNU •  Il valore atteso e’ invece Φ=129+8

-6SNU

Valutazione di eventuali sistematiche •  Per valutare l’efficienza di raccolta del Ge •  E’ stata iniettata una quantita’ nota di 71As; •  71As decade in 71Ge; •  E’ stato possibile fare questo test solo alla fine per non

contaminare il rivelatore con As; •  RISULTATO: efficienza=(100±1)%

•  Per valutare l’efficienza globale alla rivelazione di ν•  E’ stata inserita una sorgente di 51Cr (attivita’ > 60PBq) •  La sorgente produce neutrini elettronici di energia < 1 MeV

tramite il decadimento

RISULTATO: efficienza= 95 ± 8%

Ne segue che il deficit di neutrini osservato e’ REALE non e’ dovuto a problemi sperimentali

51Cr + e� ! 51V+ ⌫e E = 750 keV (90%) E = 430 keV (10%)<latexit sha1_base64="n8LxTymFuKMcwptdM38xuIPogac=">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</latexit><latexit sha1_base64="n8LxTymFuKMcwptdM38xuIPogac=">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</latexit><latexit sha1_base64="n8LxTymFuKMcwptdM38xuIPogac=">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</latexit><latexit sha1_base64="n8LxTymFuKMcwptdM38xuIPogac=">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</latexit>

Riassumendo •  Gli esperimenti radiochimici (Homestake, Gallex/GNO, Sage)

hanno fornito la prima misura del flusso di neutrini proveniente dal sole;

•  Homestake e’ sensibile a tutte le sorgenti di neutrino a parte pp e vede circa 1/3 del flusso atteso;

•  Gallex/GNO e Sage sono sensibili a tutte le sorgenti di neutrino incluso il pp e vedono circa 1/2 del flusso atteso;

•  La tecnica radiochimica impiegata da questi esperimenti NON consente di avere un’indicazione sull’energia e sulla direzione dei neutrini; rende inoltre difficile valutare eventuali variazioni stagionali e/o giorno/notte del flusso.

•  Questi esperimenti hanno permesso in ogni caso di evidenziare il cosiddetto PROBLEMA DEL NEUTRINO SOLARE

Esperimenti in tempo reale: Kamiokande….

•  Costruito nella miniera di Kamioka (in Giappone);

•  Scopo originario e’ quello di studiare la vita media del protone (1984);

•  Fisica dei neutrini solari dal 1988 al 1995;

•  E’ costituito da una grande tanica contenente 2000 tonnellate di H20;

•  1000 tubi fotomoltiplicatori;

Esperimenti in tempo reale: Kamiokande…. Sfrutta la reazione:

•  In questo caso la reazione non ha un energia minima di soglia MA

•  La necessita’ di ridurre il fondo radioattivo impone una soglia di ~7.5 MeV;

•  Kamiokande e’ sensibile solo ai ν da 8B;

Inoltre a differenza degli esperimenti radiochimici, e’ sensibile a tutti i sapori di neutrino anche se con sezioni d’urto diverse

⌫x + e� ! ⌫x + e�<latexit sha1_base64="y/xDyKa8U5eVnHBOQcOenOH/O3g=">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</latexit><latexit sha1_base64="y/xDyKa8U5eVnHBOQcOenOH/O3g=">AAACFnicdVDLSgMxFM3UV62vqks3wSII0jIpYttdwY3LCvYBnbFk0kwbmskMSUYtQ7/Cjb/ixoUibsWdf2OmrVBFDwQO59zLzTlexJnStv1pZZaWV1bXsuu5jc2t7Z387l5LhbEktElCHsqOhxXlTNCmZprTTiQpDjxO297oPPXbN1QqFoorPY6oG+CBYD4jWBuply86AdZDGSSOiHt38ATS6yJ0JBsMNZYyvIUL+gT28gW7ZNs2QgimBFXObENqtWoZVSFKLYMCmKPRy384/ZDEARWacKxUF9mRdhMsNSOcTnJOrGiEyQgPaNdQgQOq3GQaawKPjNKHfijNExpO1cWNBAdKjQPPTKYh1G8vFf/yurH2q27CRBRrKsjskB9zqEOYdgT7TFKi+dgQTCQzf4VkiCUm2jSZMyV8J4X/k1a5hAy/PC3Ua/M6suAAHIJjgEAF1MEFaIAmIOAePIJn8GI9WE/Wq/U2G81Y85198APW+xenkJ5e</latexit><latexit sha1_base64="y/xDyKa8U5eVnHBOQcOenOH/O3g=">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</latexit><latexit sha1_base64="y/xDyKa8U5eVnHBOQcOenOH/O3g=">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</latexit>

E ⇡ 10MeV<latexit sha1_base64="3H8MA+gTvi7sccpAXp+pA1weaCI=">AAACA3icdZDLSgMxFIYz9VbrbdSdboJFcCElKWLbXUEEN0IFe4HOUDJppg3NXEgyYhkKbnwVNy4UcetLuPNtzLQVVPRA4OP/zyHn/F4suNIIfVi5hcWl5ZX8amFtfWNzy97eaakokZQ1aSQi2fGIYoKHrKm5FqwTS0YCT7C2NzrL/PYNk4pH4bUex8wNyCDkPqdEG6ln7zkB0UMZpOfQIXEso1uIkXN8yVqTnl1EJYQQxhhmgCunyECtVi3jKsSZZaoI5tXo2e9OP6JJwEJNBVGqi1Gs3ZRIzalgk4KTKBYTOiID1jUYkoApN53eMIGHRulDP5LmhRpO1e8TKQmUGgee6cw2Vr+9TPzL6ybar7opD+NEs5DOPvITAXUEs0Bgn0tGtRgbIFRysyukQyIJ1Sa2ggnh61L4P7TKJWz46qRYr83jyIN9cACOAAYVUAcXoAGagII78ACewLN1bz1aL9brrDVnzWd2wY+y3j4BHbiXJQ==</latexit><latexit sha1_base64="3H8MA+gTvi7sccpAXp+pA1weaCI=">AAACA3icdZDLSgMxFIYz9VbrbdSdboJFcCElKWLbXUEEN0IFe4HOUDJppg3NXEgyYhkKbnwVNy4UcetLuPNtzLQVVPRA4OP/zyHn/F4suNIIfVi5hcWl5ZX8amFtfWNzy97eaakokZQ1aSQi2fGIYoKHrKm5FqwTS0YCT7C2NzrL/PYNk4pH4bUex8wNyCDkPqdEG6ln7zkB0UMZpOfQIXEso1uIkXN8yVqTnl1EJYQQxhhmgCunyECtVi3jKsSZZaoI5tXo2e9OP6JJwEJNBVGqi1Gs3ZRIzalgk4KTKBYTOiID1jUYkoApN53eMIGHRulDP5LmhRpO1e8TKQmUGgee6cw2Vr+9TPzL6ybar7opD+NEs5DOPvITAXUEs0Bgn0tGtRgbIFRysyukQyIJ1Sa2ggnh61L4P7TKJWz46qRYr83jyIN9cACOAAYVUAcXoAGagII78ACewLN1bz1aL9brrDVnzWd2wY+y3j4BHbiXJQ==</latexit><latexit sha1_base64="3H8MA+gTvi7sccpAXp+pA1weaCI=">AAACA3icdZDLSgMxFIYz9VbrbdSdboJFcCElKWLbXUEEN0IFe4HOUDJppg3NXEgyYhkKbnwVNy4UcetLuPNtzLQVVPRA4OP/zyHn/F4suNIIfVi5hcWl5ZX8amFtfWNzy97eaakokZQ1aSQi2fGIYoKHrKm5FqwTS0YCT7C2NzrL/PYNk4pH4bUex8wNyCDkPqdEG6ln7zkB0UMZpOfQIXEso1uIkXN8yVqTnl1EJYQQxhhmgCunyECtVi3jKsSZZaoI5tXo2e9OP6JJwEJNBVGqi1Gs3ZRIzalgk4KTKBYTOiID1jUYkoApN53eMIGHRulDP5LmhRpO1e8TKQmUGgee6cw2Vr+9TPzL6ybar7opD+NEs5DOPvITAXUEs0Bgn0tGtRgbIFRysyukQyIJ1Sa2ggnh61L4P7TKJWz46qRYr83jyIN9cACOAAYVUAcXoAGagII78ACewLN1bz1aL9brrDVnzWd2wY+y3j4BHbiXJQ==</latexit><latexit sha1_base64="3H8MA+gTvi7sccpAXp+pA1weaCI=">AAACA3icdZDLSgMxFIYz9VbrbdSdboJFcCElKWLbXUEEN0IFe4HOUDJppg3NXEgyYhkKbnwVNy4UcetLuPNtzLQVVPRA4OP/zyHn/F4suNIIfVi5hcWl5ZX8amFtfWNzy97eaakokZQ1aSQi2fGIYoKHrKm5FqwTS0YCT7C2NzrL/PYNk4pH4bUex8wNyCDkPqdEG6ln7zkB0UMZpOfQIXEso1uIkXN8yVqTnl1EJYQQxhhmgCunyECtVi3jKsSZZaoI5tXo2e9OP6JJwEJNBVGqi1Gs3ZRIzalgk4KTKBYTOiID1jUYkoApN53eMIGHRulDP5LmhRpO1e8TKQmUGgee6cw2Vr+9TPzL6ybar7opD+NEs5DOPvITAXUEs0Bgn0tGtRgbIFRysyukQyIJ1Sa2ggnh61L4P7TKJWz46qRYr83jyIN9cACOAAYVUAcXoAGagII78ACewLN1bz1aL9brrDVnzWd2wY+y3j4BHbiXJQ==</latexit>

� ⇡ 10�43 cm2<latexit sha1_base64="49x+r9fF8sOTzNrjZ0L46jYnraw=">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</latexit><latexit sha1_base64="49x+r9fF8sOTzNrjZ0L46jYnraw=">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</latexit><latexit sha1_base64="49x+r9fF8sOTzNrjZ0L46jYnraw=">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</latexit><latexit sha1_base64="49x+r9fF8sOTzNrjZ0L46jYnraw=">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</latexit>

…e… SuperKamiokande

•  E’ una versione gigante di Kamiokande;

•  Cilindro di h=41m; d=40m •  Vtot=50000 tonnellate; •  11000 tubi fotomoltiplicatori; •  Ha cominciato a prendere

dati nel 1996; •  Come Kamiokande e’

sensibile solo ai neutrini di alta energia (8B);

•  Sono in realta’ riusciti ad abbassare la soglia da 7.5 a 5 MeV;

Istallazione dei fototubi (PMT) in SuperK: I fototubi venivano istallati con l’uso di un battello, man mano che il rivelatore veniva riempito d’acqua si rendevano accessibili diverse zone del rivelatore.

Fototubo; Ø=50cm

Come funzionano Kamiokande e SuperKamiokande?

νx

• L’elettrone emesso dalla reazione di scattering emette luce Cerenkov nell’acqua (per energie >250keV);

• Questa luce viene rivelata dai tubi fotomoltiplicatori montati sulle parete della tanica;

• La caratteristica forma a cono della luce Cerenkov permette di individuare la traiettoria dell’elettrone;

• A sua volta la traiettoria dell’elettrone e’ fortemente correlata (per E> qualche MeV) con la direzione del neutrino incidente;

θ

SuperKamiokande

⌫x + e� ! ⌫x + e�<latexit sha1_base64="C7ccNgNlshOIcx+rfXVeAe8l+gg=">AAACFnicbVDLSgMxFM3UV62vUZdugkUQpGVGBF0W3LisYB/QGYdMmmlDk8yQZNQy9Cvc+CtuXCjiVtz5N2baWWjrgcDhnHu5OSdMGFXacb6t0tLyyupaeb2ysbm1vWPv7rVVnEpMWjhmseyGSBFGBWlpqhnpJpIgHjLSCUeXud+5I1LRWNzocUJ8jgaCRhQjbaTArnkc6aHkmSfS4AGekNsa9CQdDDWSMr6HhQxzfVIJ7KpTd6aAi8QtSBUUaAb2l9ePccqJ0JghpXquk2g/Q1JTzMik4qWKJAiP0ID0DBWIE+Vn01gTeGSUPoxiaZ7QcKr+3sgQV2rMQzOZh1DzXi7+5/VSHV34GRVJqonAs0NRyqCOYd4R7FNJsGZjQxCW1PwV4iGSCGvTZF6COx95kbRP667h12fVhlPUUQYH4BAcAxecgwa4Ak3QAhg8gmfwCt6sJ+vFerc+ZqMlq9jZB39gff4APHOeCQ==</latexit><latexit sha1_base64="C7ccNgNlshOIcx+rfXVeAe8l+gg=">AAACFnicbVDLSgMxFM3UV62vUZdugkUQpGVGBF0W3LisYB/QGYdMmmlDk8yQZNQy9Cvc+CtuXCjiVtz5N2baWWjrgcDhnHu5OSdMGFXacb6t0tLyyupaeb2ysbm1vWPv7rVVnEpMWjhmseyGSBFGBWlpqhnpJpIgHjLSCUeXud+5I1LRWNzocUJ8jgaCRhQjbaTArnkc6aHkmSfS4AGekNsa9CQdDDWSMr6HhQxzfVIJ7KpTd6aAi8QtSBUUaAb2l9ePccqJ0JghpXquk2g/Q1JTzMik4qWKJAiP0ID0DBWIE+Vn01gTeGSUPoxiaZ7QcKr+3sgQV2rMQzOZh1DzXi7+5/VSHV34GRVJqonAs0NRyqCOYd4R7FNJsGZjQxCW1PwV4iGSCGvTZF6COx95kbRP667h12fVhlPUUQYH4BAcAxecgwa4Ak3QAhg8gmfwCt6sJ+vFerc+ZqMlq9jZB39gff4APHOeCQ==</latexit><latexit sha1_base64="C7ccNgNlshOIcx+rfXVeAe8l+gg=">AAACFnicbVDLSgMxFM3UV62vUZdugkUQpGVGBF0W3LisYB/QGYdMmmlDk8yQZNQy9Cvc+CtuXCjiVtz5N2baWWjrgcDhnHu5OSdMGFXacb6t0tLyyupaeb2ysbm1vWPv7rVVnEpMWjhmseyGSBFGBWlpqhnpJpIgHjLSCUeXud+5I1LRWNzocUJ8jgaCRhQjbaTArnkc6aHkmSfS4AGekNsa9CQdDDWSMr6HhQxzfVIJ7KpTd6aAi8QtSBUUaAb2l9ePccqJ0JghpXquk2g/Q1JTzMik4qWKJAiP0ID0DBWIE+Vn01gTeGSUPoxiaZ7QcKr+3sgQV2rMQzOZh1DzXi7+5/VSHV34GRVJqonAs0NRyqCOYd4R7FNJsGZjQxCW1PwV4iGSCGvTZF6COx95kbRP667h12fVhlPUUQYH4BAcAxecgwa4Ak3QAhg8gmfwCt6sJ+vFerc+ZqMlq9jZB39gff4APHOeCQ==</latexit><latexit sha1_base64="C7ccNgNlshOIcx+rfXVeAe8l+gg=">AAACFnicbVDLSgMxFM3UV62vUZdugkUQpGVGBF0W3LisYB/QGYdMmmlDk8yQZNQy9Cvc+CtuXCjiVtz5N2baWWjrgcDhnHu5OSdMGFXacb6t0tLyyupaeb2ysbm1vWPv7rVVnEpMWjhmseyGSBFGBWlpqhnpJpIgHjLSCUeXud+5I1LRWNzocUJ8jgaCRhQjbaTArnkc6aHkmSfS4AGekNsa9CQdDDWSMr6HhQxzfVIJ7KpTd6aAi8QtSBUUaAb2l9ePccqJ0JghpXquk2g/Q1JTzMik4qWKJAiP0ID0DBWIE+Vn01gTeGSUPoxiaZ7QcKr+3sgQV2rMQzOZh1DzXi7+5/VSHV34GRVJqonAs0NRyqCOYd4R7FNJsGZjQxCW1PwV4iGSCGvTZF6COx95kbRP667h12fVhlPUUQYH4BAcAxecgwa4Ak3QAhg8gmfwCt6sJ+vFerc+ZqMlq9jZB39gff4APHOeCQ==</latexit>

Esempio di evento di neutrino solare registrato in SuperK (12 Marzo 1998)

La scala di colori indica il tempo

Risultati di Superkamiokande

• Vede circa 15 neutrini al giorno;

• Corrispondenti a Φ=2.35±0.02(stat)±0.08(sys)x106 cm-2 s-1

E’ circa la meta’ del flusso previsto!

Risoluzione in Energia: 14% (@ 10MeV)

Spettro compatibile con la forma attesa

•  SuperK e’ in grado di: –  Contare il numero di neutrini solari della sorgente 8B; –  Misurare l’energia dell’elettrone uscente; –  Misurare la direzione dell’elettrone uscente; –  Valutare variazioni temporali del segnale di neutrino;

Misura delle variazioni stagionali del flusso di neutrini solari dovute

all’eccentricita’ dell’orbita terrestre

Giugno

t=T/2

Marzo

t=T/4

Dicembre

t=0

Settembre

t=3/4T

L0= 1 a.u.

T=1 anno

E=0.0167

L(t) = L0

✓1� ✏ cos

2⇡t

T

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Homestake SuperK Gallex

Riassumendo: il problema del neutrino solare

I 3 problemi del neutrino solare 1)  Tutti gli esperimenti vedono un

flusso significativamente inferiore a quello previsto (1/2 o 1/3);

2)  I risultati di SuperK e Homestake sono inconsistenti fra di loro;

3) Gallex misura un flusso consistente con la sola sorgente pp (e’ quella prevista con maggiore precisione in quanto direttamente legata alla luminosita’ solare): non c’e’ spazio per gli altri tipi di neutrino;

QUAL’E’ LA SOLUZIONE DEL PROBLEMA DEL NEUTRINO SOLARE?

La soluzione: oscillazioni di neutrino CONCETTO BASE: gli autostati di neutrino delle interazioni

deboli NON sono autostati di massa;

STATI DI SAPORE Produzione e rivelazione dei ν

STATI DI MASSA Propagazione dei ν

MATRICE DI MIXING

CASO A DUE SAPORI:

Angolo di mixing

⌫f =

✓⌫e⌫µ

◆

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⌫p =

✓⌫1⌫2

◆

<latexit sha1_base64="N8md+7XoBT523G4E8o7AzfFyTbo=">AAACNnicbVDLSsNAFJ34Nr6qLt0MFkE3koigLgTBjRuhgn1AU8tketMOTiZh5kYooV/lxu9w140LRdz6CU7aLHxdGO7hnPuYe8JUCoOeN3ZmZufmFxaXlt2V1bX1jcrmVsMkmeZQ54lMdCtkBqRQUEeBElqpBhaHEprh/WWhNx9AG5GoWxym0IlZX4lIcIaW6laug5jhQMd5oLK7lJ5TN5AQ4b4bhNAXKmdas+Eo5yPXFnT9IJjkoyKD6pWyG2jRH+DBqFupeofeJOhf4JegSsqodSvPQS/hWQwKuWTGtH0vxY4di4JLsIMzAynj96wPbQsVi8F08snZI7pnmR6NEm2fQjphv3fkLDZmGIe2sjjS/NYK8j+tnWF02smFSjMExaeLokxSTGjhIe0JDRzl0ALGtbB/pXzANONonXatCf7vk/+CxtGhb/HNcfXirLRjieyQXbJPfHJCLsgVqZE64eSRjMkreXOenBfn3fmYls44Zc82+RHO5xdRB6ul</latexit><latexit sha1_base64="N8md+7XoBT523G4E8o7AzfFyTbo=">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</latexit><latexit sha1_base64="N8md+7XoBT523G4E8o7AzfFyTbo=">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</latexit><latexit sha1_base64="N8md+7XoBT523G4E8o7AzfFyTbo=">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</latexit>

U =

✓cos ✓ sin ✓� sin ✓ cos ✓

◆

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⌫f = U ⌫p<latexit sha1_base64="7ZG4P9MbJ9YGAL27bOfW1xVBtns=">AAACDHicbVDLSsNAFJ3UV62vqks3g0VwISURQV0IBTcuK5i20MQymU7aoTOTMDMRSsgHuPFX3LhQxK0f4M6/cZJmoa0HBs6ccy/33hPEjCpt299WZWl5ZXWtul7b2Nza3qnv7nVUlEhMXByxSPYCpAijgriaakZ6sSSIB4x0g8l17ncfiFQ0End6GhOfo5GgIcVIG2lQb3gc6bHkqSeS+xBeweKPEUvdzDvJxTgzVXbTLgAXiVOSBijRHtS/vGGEE06Exgwp1XfsWPspkppiRrKalygSIzxBI9I3VCBOlJ8Wx2TwyChDGEbSPKFhof7uSBFXasoDU5mvqua9XPzP6yc6vPBTKuJEE4Fng8KEQR3BPBk4pJJgzaaGICyp2RXiMZIIa5NfzYTgzJ+8SDqnTcfw27NG67KMowoOwCE4Bg44By1wA9rABRg8gmfwCt6sJ+vFerc+ZqUVq+zZB39gff4A3YmbdQ==</latexit><latexit sha1_base64="7ZG4P9MbJ9YGAL27bOfW1xVBtns=">AAACDHicbVDLSsNAFJ3UV62vqks3g0VwISURQV0IBTcuK5i20MQymU7aoTOTMDMRSsgHuPFX3LhQxK0f4M6/cZJmoa0HBs6ccy/33hPEjCpt299WZWl5ZXWtul7b2Nza3qnv7nVUlEhMXByxSPYCpAijgriaakZ6sSSIB4x0g8l17ncfiFQ0End6GhOfo5GgIcVIG2lQb3gc6bHkqSeS+xBeweKPEUvdzDvJxTgzVXbTLgAXiVOSBijRHtS/vGGEE06Exgwp1XfsWPspkppiRrKalygSIzxBI9I3VCBOlJ8Wx2TwyChDGEbSPKFhof7uSBFXasoDU5mvqua9XPzP6yc6vPBTKuJEE4Fng8KEQR3BPBk4pJJgzaaGICyp2RXiMZIIa5NfzYTgzJ+8SDqnTcfw27NG67KMowoOwCE4Bg44By1wA9rABRg8gmfwCt6sJ+vFerc+ZqUVq+zZB39gff4A3YmbdQ==</latexit><latexit sha1_base64="7ZG4P9MbJ9YGAL27bOfW1xVBtns=">AAACDHicbVDLSsNAFJ3UV62vqks3g0VwISURQV0IBTcuK5i20MQymU7aoTOTMDMRSsgHuPFX3LhQxK0f4M6/cZJmoa0HBs6ccy/33hPEjCpt299WZWl5ZXWtul7b2Nza3qnv7nVUlEhMXByxSPYCpAijgriaakZ6sSSIB4x0g8l17ncfiFQ0End6GhOfo5GgIcVIG2lQb3gc6bHkqSeS+xBeweKPEUvdzDvJxTgzVXbTLgAXiVOSBijRHtS/vGGEE06Exgwp1XfsWPspkppiRrKalygSIzxBI9I3VCBOlJ8Wx2TwyChDGEbSPKFhof7uSBFXasoDU5mvqua9XPzP6yc6vPBTKuJEE4Fng8KEQR3BPBk4pJJgzaaGICyp2RXiMZIIa5NfzYTgzJ+8SDqnTcfw27NG67KMowoOwCE4Bg44By1wA9rABRg8gmfwCt6sJ+vFerc+ZqUVq+zZB39gff4A3YmbdQ==</latexit><latexit sha1_base64="7ZG4P9MbJ9YGAL27bOfW1xVBtns=">AAACDHicbVDLSsNAFJ3UV62vqks3g0VwISURQV0IBTcuK5i20MQymU7aoTOTMDMRSsgHuPFX3LhQxK0f4M6/cZJmoa0HBs6ccy/33hPEjCpt299WZWl5ZXWtul7b2Nza3qnv7nVUlEhMXByxSPYCpAijgriaakZ6sSSIB4x0g8l17ncfiFQ0End6GhOfo5GgIcVIG2lQb3gc6bHkqSeS+xBeweKPEUvdzDvJxTgzVXbTLgAXiVOSBijRHtS/vGGEE06Exgwp1XfsWPspkppiRrKalygSIzxBI9I3VCBOlJ8Wx2TwyChDGEbSPKFhof7uSBFXasoDU5mvqua9XPzP6yc6vPBTKuJEE4Fng8KEQR3BPBk4pJJgzaaGICyp2RXiMZIIa5NfzYTgzJ+8SDqnTcfw27NG67KMowoOwCE4Bg44By1wA9rABRg8gmfwCt6sJ+vFerc+ZqUVq+zZB39gff4A3YmbdQ==</latexit>

Propagazione nel vuoto

Allora la probabilita’ di avere un |νe ,t> venga rivelato come νµ e’ data da:

Suppongo di avere un νe al tempo t=0

Dopo un tempo t avro’:

Noto che nell’ipotesi ultrarelativistica:

Ecco dove entra la massa! E’ quella che “disallinea” I due autostati. Se fosse =0 non si avrebbero oscillazioni!

⌫f = U ⌫p<latexit sha1_base64="7ZG4P9MbJ9YGAL27bOfW1xVBtns=">AAACDHicbVDLSsNAFJ3UV62vqks3g0VwISURQV0IBTcuK5i20MQymU7aoTOTMDMRSsgHuPFX3LhQxK0f4M6/cZJmoa0HBs6ccy/33hPEjCpt299WZWl5ZXWtul7b2Nza3qnv7nVUlEhMXByxSPYCpAijgriaakZ6sSSIB4x0g8l17ncfiFQ0End6GhOfo5GgIcVIG2lQb3gc6bHkqSeS+xBeweKPEUvdzDvJxTgzVXbTLgAXiVOSBijRHtS/vGGEE06Exgwp1XfsWPspkppiRrKalygSIzxBI9I3VCBOlJ8Wx2TwyChDGEbSPKFhof7uSBFXasoDU5mvqua9XPzP6yc6vPBTKuJEE4Fng8KEQR3BPBk4pJJgzaaGICyp2RXiMZIIa5NfzYTgzJ+8SDqnTcfw27NG67KMowoOwCE4Bg44By1wA9rABRg8gmfwCt6sJ+vFerc+ZqUVq+zZB39gff4A3YmbdQ==</latexit><latexit sha1_base64="7ZG4P9MbJ9YGAL27bOfW1xVBtns=">AAACDHicbVDLSsNAFJ3UV62vqks3g0VwISURQV0IBTcuK5i20MQymU7aoTOTMDMRSsgHuPFX3LhQxK0f4M6/cZJmoa0HBs6ccy/33hPEjCpt299WZWl5ZXWtul7b2Nza3qnv7nVUlEhMXByxSPYCpAijgriaakZ6sSSIB4x0g8l17ncfiFQ0End6GhOfo5GgIcVIG2lQb3gc6bHkqSeS+xBeweKPEUvdzDvJxTgzVXbTLgAXiVOSBijRHtS/vGGEE06Exgwp1XfsWPspkppiRrKalygSIzxBI9I3VCBOlJ8Wx2TwyChDGEbSPKFhof7uSBFXasoDU5mvqua9XPzP6yc6vPBTKuJEE4Fng8KEQR3BPBk4pJJgzaaGICyp2RXiMZIIa5NfzYTgzJ+8SDqnTcfw27NG67KMowoOwCE4Bg44By1wA9rABRg8gmfwCt6sJ+vFerc+ZqUVq+zZB39gff4A3YmbdQ==</latexit><latexit sha1_base64="7ZG4P9MbJ9YGAL27bOfW1xVBtns=">AAACDHicbVDLSsNAFJ3UV62vqks3g0VwISURQV0IBTcuK5i20MQymU7aoTOTMDMRSsgHuPFX3LhQxK0f4M6/cZJmoa0HBs6ccy/33hPEjCpt299WZWl5ZXWtul7b2Nza3qnv7nVUlEhMXByxSPYCpAijgriaakZ6sSSIB4x0g8l17ncfiFQ0End6GhOfo5GgIcVIG2lQb3gc6bHkqSeS+xBeweKPEUvdzDvJxTgzVXbTLgAXiVOSBijRHtS/vGGEE06Exgwp1XfsWPspkppiRrKalygSIzxBI9I3VCBOlJ8Wx2TwyChDGEbSPKFhof7uSBFXasoDU5mvqua9XPzP6yc6vPBTKuJEE4Fng8KEQR3BPBk4pJJgzaaGICyp2RXiMZIIa5NfzYTgzJ+8SDqnTcfw27NG67KMowoOwCE4Bg44By1wA9rABRg8gmfwCt6sJ+vFerc+ZqUVq+zZB39gff4A3YmbdQ==</latexit><latexit sha1_base64="7ZG4P9MbJ9YGAL27bOfW1xVBtns=">AAACDHicbVDLSsNAFJ3UV62vqks3g0VwISURQV0IBTcuK5i20MQymU7aoTOTMDMRSsgHuPFX3LhQxK0f4M6/cZJmoa0HBs6ccy/33hPEjCpt299WZWl5ZXWtul7b2Nza3qnv7nVUlEhMXByxSPYCpAijgriaakZ6sSSIB4x0g8l17ncfiFQ0End6GhOfo5GgIcVIG2lQb3gc6bHkqSeS+xBeweKPEUvdzDvJxTgzVXbTLgAXiVOSBijRHtS/vGGEE06Exgwp1XfsWPspkppiRrKalygSIzxBI9I3VCBOlJ8Wx2TwyChDGEbSPKFhof7uSBFXasoDU5mvqua9XPzP6yc6vPBTKuJEE4Fng8KEQR3BPBk4pJJgzaaGICyp2RXiMZIIa5NfzYTgzJ+8SDqnTcfw27NG67KMowoOwCE4Bg44By1wA9rABRg8gmfwCt6sJ+vFerc+ZqUVq+zZB39gff4A3YmbdQ==</latexit>

|⌫ei = cos ✓|⌫1i+ sin ✓|⌫2i<latexit sha1_base64="wNzHfkkBLRvKln8rD4Cc2PQ4350=">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</latexit><latexit sha1_base64="wNzHfkkBLRvKln8rD4Cc2PQ4350=">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</latexit><latexit sha1_base64="wNzHfkkBLRvKln8rD4Cc2PQ4350=">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</latexit><latexit sha1_base64="wNzHfkkBLRvKln8rD4Cc2PQ4350=">AAACPHicbZBNSwMxEIaz9bt+VT16CRZBEGS3COpBELx4rGhV6JaSTadtMJtdklmhbPvDvPgjvHny4kERr57NtqtY60Dg5X1mkswbxFIYdN0npzA1PTM7N79QXFxaXlktra1fmSjRHGo8kpG+CZgBKRTUUKCEm1gDCwMJ18Htacav70AbEalL7MXQCFlHibbgDK3VLF34IcOuDtO+r5ImUF8z1ZFAj6nPI0N97AIy2qcZ9X7oLvWNUOO08k0HzVLZ3XOHRSeFl4syyavaLD36rYgnISjkkhlT99wYGynTKLi9r+gnBmLGb1kH6lYqFoJppMPlB3TbOi3ajrQ9CunQ/T2RstCYXhjYzmxV85dl5n+snmD7sJEKFScIio8eaieSYkSzJGlLaOAoe1YwroX9K+VdphlHm3fRhuD9XXlSXFX2PKvP98snR3kc82STbJEd4pEDckLOSJXUCCf35Jm8kjfnwXlx3p2PUWvByWc2yFg5n19ec62F</latexit>

|⌫µi = � sin ✓|⌫1i+ cos ✓|⌫2i<latexit sha1_base64="wsSOogFl0F5HF19O7QsQ712/hlk=">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</latexit><latexit sha1_base64="wsSOogFl0F5HF19O7QsQ712/hlk=">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</latexit><latexit sha1_base64="wsSOogFl0F5HF19O7QsQ712/hlk=">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</latexit><latexit sha1_base64="wsSOogFl0F5HF19O7QsQ712/hlk=">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</latexit>

|⌫ei = cos ✓|⌫1i+ sin ✓|⌫2i<latexit sha1_base64="wNzHfkkBLRvKln8rD4Cc2PQ4350=">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</latexit><latexit sha1_base64="wNzHfkkBLRvKln8rD4Cc2PQ4350=">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</latexit><latexit sha1_base64="wNzHfkkBLRvKln8rD4Cc2PQ4350=">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</latexit><latexit sha1_base64="wNzHfkkBLRvKln8rD4Cc2PQ4350=">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</latexit>

|⌫e, ti = cos ✓ e�i E1 t|⌫1i+ sin ✓ e�i E2 t|⌫2i<latexit sha1_base64="K3BUrFlSCTk/5+eYaQUwLn1EAps=">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</latexit><latexit sha1_base64="K3BUrFlSCTk/5+eYaQUwLn1EAps=">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</latexit><latexit sha1_base64="K3BUrFlSCTk/5+eYaQUwLn1EAps=">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</latexit><latexit sha1_base64="K3BUrFlSCTk/5+eYaQUwLn1EAps=">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</latexit>

P(⌫e ! ⌫µ) = |h⌫e, t|⌫µ, 0i|2 = h⌫e, t|⌫µih⌫e, t|⌫µi⇤<latexit sha1_base64="3TLvURqqyy8tyR+xuZkrTrG4nJk=">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</latexit><latexit sha1_base64="3TLvURqqyy8tyR+xuZkrTrG4nJk=">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</latexit><latexit sha1_base64="3TLvURqqyy8tyR+xuZkrTrG4nJk=">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</latexit><latexit sha1_base64="3TLvURqqyy8tyR+xuZkrTrG4nJk=">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</latexit>

m ⌧ Ei ) Ei ' |�!p |+ m2i

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pc � mc2<latexit sha1_base64="9Pj8kJKoWdC7PSNuIOmCHdIqWAw=">AAAB/3icbVDLSsNAFL2pr1pfUcGNm8EiuCpJEdRdwY3LCvYBTSyT6aQdOpOEmYlQYhf+ihsXirj1N9z5N07aLLT1wMDhnHu5Z06QcKa043xbpZXVtfWN8mZla3tnd8/eP2irOJWEtkjMY9kNsKKcRbSlmea0m0iKRcBpJxhf537ngUrF4uhOTxLqCzyMWMgI1kbq20eewHokRZYggrzhEAlE7uvTvl11as4MaJm4BalCgWbf/vIGMUkFjTThWKme6yTaz7DUjHA6rXipogkmYzykPUMjLKjys1n+KTo1ygCFsTQv0mim/t7IsFBqIgIzmadVi14u/uf1Uh1e+hmLklTTiMwPhSlHOkZ5GWjAJCWaTwzBRDKTFZERlphoU1nFlOAufnmZtOs11/Db82rjqqijDMdwAmfgwgU04Aaa0AICj/AMr/BmPVkv1rv1MR8tWcXOIfyB9fkDu1OVOA==</latexit><latexit sha1_base64="9Pj8kJKoWdC7PSNuIOmCHdIqWAw=">AAAB/3icbVDLSsNAFL2pr1pfUcGNm8EiuCpJEdRdwY3LCvYBTSyT6aQdOpOEmYlQYhf+ihsXirj1N9z5N07aLLT1wMDhnHu5Z06QcKa043xbpZXVtfWN8mZla3tnd8/eP2irOJWEtkjMY9kNsKKcRbSlmea0m0iKRcBpJxhf537ngUrF4uhOTxLqCzyMWMgI1kbq20eewHokRZYggrzhEAlE7uvTvl11as4MaJm4BalCgWbf/vIGMUkFjTThWKme6yTaz7DUjHA6rXipogkmYzykPUMjLKjys1n+KTo1ygCFsTQv0mim/t7IsFBqIgIzmadVi14u/uf1Uh1e+hmLklTTiMwPhSlHOkZ5GWjAJCWaTwzBRDKTFZERlphoU1nFlOAufnmZtOs11/Db82rjqqijDMdwAmfgwgU04Aaa0AICj/AMr/BmPVkv1rv1MR8tWcXOIfyB9fkDu1OVOA==</latexit><latexit sha1_base64="9Pj8kJKoWdC7PSNuIOmCHdIqWAw=">AAAB/3icbVDLSsNAFL2pr1pfUcGNm8EiuCpJEdRdwY3LCvYBTSyT6aQdOpOEmYlQYhf+ihsXirj1N9z5N07aLLT1wMDhnHu5Z06QcKa043xbpZXVtfWN8mZla3tnd8/eP2irOJWEtkjMY9kNsKKcRbSlmea0m0iKRcBpJxhf537ngUrF4uhOTxLqCzyMWMgI1kbq20eewHokRZYggrzhEAlE7uvTvl11as4MaJm4BalCgWbf/vIGMUkFjTThWKme6yTaz7DUjHA6rXipogkmYzykPUMjLKjys1n+KTo1ygCFsTQv0mim/t7IsFBqIgIzmadVi14u/uf1Uh1e+hmLklTTiMwPhSlHOkZ5GWjAJCWaTwzBRDKTFZERlphoU1nFlOAufnmZtOs11/Db82rjqqijDMdwAmfgwgU04Aaa0AICj/AMr/BmPVkv1rv1MR8tWcXOIfyB9fkDu1OVOA==</latexit><latexit sha1_base64="9Pj8kJKoWdC7PSNuIOmCHdIqWAw=">AAAB/3icbVDLSsNAFL2pr1pfUcGNm8EiuCpJEdRdwY3LCvYBTSyT6aQdOpOEmYlQYhf+ihsXirj1N9z5N07aLLT1wMDhnHu5Z06QcKa043xbpZXVtfWN8mZla3tnd8/eP2irOJWEtkjMY9kNsKKcRbSlmea0m0iKRcBpJxhf537ngUrF4uhOTxLqCzyMWMgI1kbq20eewHokRZYggrzhEAlE7uvTvl11as4MaJm4BalCgWbf/vIGMUkFjTThWKme6yTaz7DUjHA6rXipogkmYzykPUMjLKjys1n+KTo1ygCFsTQv0mim/t7IsFBqIgIzmadVi14u/uf1Uh1e+hmLklTTiMwPhSlHOkZ5GWjAJCWaTwzBRDKTFZERlphoU1nFlOAufnmZtOs11/Db82rjqqijDMdwAmfgwgU04Aaa0AICj/AMr/BmPVkv1rv1MR8tWcXOIfyB9fkDu1OVOA==</latexit>

P (⌫e ! ⌫µ) = h⌫e, t|⌫µ, 0i|h⌫e, t|⌫µ, 0i|⇤ =

⇥� cos ✓ sin ✓ e�iE1t + sin ✓ cos ✓ e�iE2t

⇤ ⇥� cos ✓ sin ✓ e+iE1t + sin ✓ cos ✓ e+iE2t

⇤=

2 cos2 ✓ sin2 ✓ � cos2 ✓ sin2 ✓⇥e�i(E1�E2)t + e+i(E1�E2)t

⇤=

2�sin 2✓

2

�2 � 2�sin 2✓

2

�2cos(E1 � E2)t =

12 sin

2 2✓[1� cos(E1 � E2)] = sin2 2✓ sin2 (E1�E2)t2 = sin2 2✓ sin2 �E

2c L<latexit sha1_base64="+K+8qPY5B4mkixTAZtSF7e4DRbA=">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</latexit><latexit sha1_base64="x9uw8SwKZPZAVeNnBxdaIdMcLA0=">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</latexit><latexit sha1_base64="x9uw8SwKZPZAVeNnBxdaIdMcLA0=">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</latexit><latexit sha1_base64="PvTiV+zz82jWQ26xnPXcWRLmAhk=">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</latexit>

Usando le formule

Ricordando che:

Si ottiene:

2 sin ✓ cos ✓ = sin 2✓e�i✓+e+i✓

2 = cos 2✓q1�cos ✓

2 = sin 2✓<latexit sha1_base64="1apf3vIKIZLq+e5w6EBf9MjPV8Y=">AAACl3icbVHLatwwFJXdtEndR6aPTchGNBQKIcH2JqUQmpISskygkwRG00HWXM+IyLIrXRcG4Z/Ih+Qbss22u/5N5fGEvHpBcO65T52bVUpajOO/Qfhk6emz5ZXn0YuXr16v9t68PbFlbQT0RalKc5ZxC0pq6KNEBWeVAV5kCk6z8/02fvobjJWl/oGzCoYFn2iZS8HRU6PeJSs4Tk3hWAYTqR03hs8ap5ooZVZqhlNAzkRpO0R3aUvTdOEyFrHccOHgp9uSHdlsemfzxmlc2uy2De7V2F8GXVeZbN22b5N99t0JEQM9XqzVRKPeRrwdz40+BskCbOx9u764IoQcjXp/2LgUdQEaheLWDpK4wqHvh1IoaCJWW6i4OOcTGHioeQF26Oa6NvSjZ8Y0L41/GumcvVvheGHtrMh8ZquifRhryf/FBjXmn4dO6qpG0KIblNeKYknbI9GxNCBQzTzgwki/KxVT7tVCf8pWhOThlx+Dk3Q78fjYq5GSzlbIOvlAPpGE7JA9ckiOSJ+I4H3wJdgPvodr4dfwIDzsUsNgUfOO3LPw+B/b8c5s</latexit><latexit sha1_base64="i02CfCI6OPRFlPdyVrUC6oZ+A/Q=">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</latexit><latexit sha1_base64="i02CfCI6OPRFlPdyVrUC6oZ+A/Q=">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</latexit><latexit sha1_base64="OOvn/p71sXgNzYlTSgDDIVwHbYk=">AAACl3icbVHbatwwEJXdW+Jesm3zEvoiuhQKIcH2S0MhJJAS8phANwmstousHe+KyLIjjQOL8C/1Y/rWv6m8dsitA4IzZ646k1VKWozjv0H47PmLl6/W1qPXb96+2xi8/3Buy9oIGIlSleYy4xaU1DBCiQouKwO8yBRcZFdHbfziBoyVpf6JywomBZ9rmUvB0VPTwW9WcFyYwrEM5lI7bgxfNk41Ucqs1AwXgJyJ0naI7tOWpmnvMhax3HDh4JfbkR3ZbHtn+9ZpXNrstw0e1Nhrg66rTHbu2rfJPvv+hIiBnvVrNdF0MIx345XRpyDpwZD0djod/GGzUtQFaBSKWztO4gonvh9KoaCJWG2h4uKKz2HsoeYF2Ilb6drQL56Z0bw0/mmkK/Z+heOFtcsi85mtivZxrCX/FxvXmO9NnNRVjaBFNyivFcWStkeiM2lAoFp6wIWRflcqFtyrhf6UrQjJ4y8/BefpbuLxWTw8THs51sgn8pl8JQn5Rg7JCTklIyKCzeB7cBT8CLfCg/A4POlSw6Cv+UgeWHj2D1Y9y9A=</latexit>

|⌫e, ti = cos ✓ e�iE1t|⌫1i+ sin ✓ e�iE2t|⌫2i<latexit sha1_base64="htan67U0mhF0ZsO9bdkFZ7T+Fow=">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</latexit><latexit sha1_base64="htan67U0mhF0ZsO9bdkFZ7T+Fow=">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</latexit><latexit sha1_base64="htan67U0mhF0ZsO9bdkFZ7T+Fow=">AAACUHicbVHPSxtBFH6bVquxamxP4mVQhII/2M2lehAEETxaMCpk4jI7eUkGZ2eXmbdCWAP9B3vx5t/hpQfFziYR2tgPhvn43vdm5n2T5Fo5CsPHoPbh49z8p4XF+tLn5ZXVxtqXS5cVVmJLZjqz14lwqJXBFinSeJ1bFGmi8Sq5PanqV3doncrMBQ1z7KSib1RPSUFeiht9ngoa2LRk99wUMe4St8L0NbIjxmXmGKcBkuC7eFPuqdM4otHYGL3Zdhh3yszamlNbc2obxY2tcD8cg70n0ZRsHa//hArnceOBdzNZpGhIauFcOwpz6pTCkpL+vDovHOZC3oo+tj01IkXXKceBjNi2V7qsl1m/DLGx+ndHKVLnhmnindX4brZWif+rtQvqHXRKZfKC0MjJRb1CM8pYlS7rKouS9NATIa3yb2VyIKyQ5P+g7kOIZkd+Ty6b+5HnP3wahzDBAmzAJnyDCL7DMZzBObRAwi94gmd4CR6C38FrLZhY33b4Cv+gVv8DXji1SQ==</latexit><latexit sha1_base64="V0MevDKkhVcZtJH9oQyyjDnmpn0=">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</latexit>

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2E<latexit sha1_base64="UqYb04OQ82Pg/E/4Vr2HotI3EmE=">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</latexit><latexit 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sha1_base64="ck8pdC+ekZH4nUmSP+ZG7r8lEyk=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odOn4MoA7ncAFXEMIN3MEDdKALAhJ4hXdv4r15H6uuat66tDP4I+/zBzjGijg=</latexit><latexit 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sha1_base64="VrQZlE3NzISQhZRrKlft9ucxJMg=">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</latexit><latexit sha1_base64="NiKSKbK54znFBamxEGFBD9WUDKg=">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</latexit><latexit sha1_base64="UqYb04OQ82Pg/E/4Vr2HotI3EmE=">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</latexit><latexit 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sha1_base64="UqYb04OQ82Pg/E/4Vr2HotI3EmE=">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</latexit><latexit 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sha1_base64="UqYb04OQ82Pg/E/4Vr2HotI3EmE=">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</latexit>

dove Losc = 2.48

✓E

MeV

◆✓eV2

�m2

◆

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P(⌫e ! ⌫µ) = sin2 2✓ sin2✓1.267

L�m2

E

◆= sin2 2✓ sin2

⇡ L

Losc

!

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La probabilita’ di oscillazione dipende da: •  L’angolo di mixing θ; •  L’energia del neutrino E; •  Il percorso compiuto L; •  La differenza del quadrato delle masse dei neutrini Δm2=m2

2 –m21;

Oscillazioni nel vuoto: riassumendo I neutrini elettronici prodotti all’interno del sole possono subire una trasformazione nel loro percorso verso la terra e trasformarsi in neutrini di altri sapori;

Noto!!

Nota!!

Nell’ipotesi di oscillazione nel vuoto, dai risultati sperimentali e’ possibile ricavarsi l’angolo di mixing θ e Δm2!

P(⌫e ! ⌫µ) = sin2 2✓ sin2⇡ L

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Losc = 2.48

✓E

MeV

◆✓eV2

�m2

◆

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Ei ' |�!p |+ m2i

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Oscillazioni nella materia •  Quando un neutrino si propaga nella materia e non nel vuoto il termine di

propagazione degli autostati di massa cambia un po’; •  Vale ancora che

•  Dove Uint e’ il potenziale che descrive le interazioni con la materia (in particolare con gli elettroni della materia);

•  Questo termine “disallinea” ancora di piu’ i neutrini, in quanto il νe , partner dell’elettrone, tendera’ ad interagire maggiormente rispetto a νµ e ντ;

•  Si puo’dimostrare che esistono particolari condizioni di risonanza per le quali la probailita’ di oscillazione e’ favorita;

•  La risonanza dipende dalla densita’ del mezzo, dall’energia del neutrino e da Δm2;

Se ho prodotto un νe al tempo t=0

Dopo un tempo t avro’:

In questo caso pero’:

|⌫ei = cos ✓ |⌫1i+ sin ✓ |⌫2i<latexit sha1_base64="VRn5HL486nGae9oR6BIJTxUb4Bw=">AAACOnicbVDPSxtBGP3W36atbvUkXgZDoWCRXS/qoSD00mMCRgOZEGYnX5LB2dll5lshbIX+V730r+ith156UKTX/gHOJhFM9MHA473vm5n3klwrR1H0O1haXlldW9/YrL15+25rO3y/c+mywkpsyUxntp0Ih1oZbJEije3cokgTjVfJ9ZfKv7pB61RmLmicYzcVQ6MGSgryUi9s8lTQyKYl+8ZN0UNuhRlqZJ8Zl5ljnEZIgn+amPGTeci4U2bePJ6Zt72wHh1FE7CXJJ6R+vned6jQ6IW/eD+TRYqGpBbOdeIop24pLCnp76vxwmEu5LUYYsdTI1J03XIS/ZZ98EqfDTLrjyE2UZ9vlCJ1bpwmfrIK6ha9SnzN6xQ0OO2WyuQFoZHThwaFZpSxqkfWVxYl6bEnQlrl/8rkSFghybdd8yXEi5Ffksvjo9jzpm/jDKbYgH04gI8Qwwmcw1doQAsk/IA/cAf3wc/gb/AQ/JuOLgWznV2YQ/D/EY9ErpY=</latexit><latexit sha1_base64="VRn5HL486nGae9oR6BIJTxUb4Bw=">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</latexit><latexit sha1_base64="VRn5HL486nGae9oR6BIJTxUb4Bw=">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</latexit><latexit sha1_base64="jkaRfp/VjN0lcwmZiTTvbGPERTQ=">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</latexit>

|⌫e, ti = cos ✓ e�iE1t|⌫1i+ sin ✓ e�iE2t|⌫2i<latexit sha1_base64="htan67U0mhF0ZsO9bdkFZ7T+Fow=">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</latexit><latexit sha1_base64="htan67U0mhF0ZsO9bdkFZ7T+Fow=">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</latexit><latexit sha1_base64="htan67U0mhF0ZsO9bdkFZ7T+Fow=">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</latexit><latexit sha1_base64="V0MevDKkhVcZtJH9oQyyjDnmpn0=">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</latexit>

Oscillazioni nella materia: riassumendo I neutrini elettronici prodotti all’interno del sole possono subire una trasformazione all’interno del sole stesso e trasformarsi in neutrini di altri sapori;

La probabilita’ di oscillazione dipende da: •  L’angolo di mixing θ; •  L’energia del neutrino E; •  Il percorso compiuto L; •  La differenza del quadrato delle masse dei ν Δm2=m2

2 –m21;

•  La densita’ ρ all’interno del sole;

Nota!! Noto!!

Nota!!

Nell’ipotesi di oscillazione nella materia, dai risultati sperimentali e’ possibile ricavarsi l’angolo di mixing θ e Δm2!

P(⌫e ! ⌫µ) = sin2 2✓M sin2⇡ L

LM<latexit sha1_base64="ko1iy3D/M7yXV7fr4bV7FSYYT64=">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</latexit><latexit sha1_base64="jP6kyVaaI0YC4/4oQlRQprEcn2I=">AAACPXicbVBBaxNBGJ2ttcbU1tQcvQyWQoVSdgNFexACXnpoIUKSFjJxmZ18mwyZmV1mvq2EZX9F/42X/gdv3kTxoIhXr84mPdTWBwNv3vs+Zt5LciUdhuHnYO3B+sONR43Hzc0nW9tPWzvPhi4rrICByFRmLxLuQEkDA5So4CK3wHWi4DyZv63980uwTmamj4scxppPjUyl4OiluNVnmuPM6rK3z0wRA7NyOkNubfahvpdMF9XLN8xJ875DO5ThDJDHZ+xgJbHUclGyXLKD06o8jc8qSqtm3NoND8Ml6H0S3ZDd7tFG+9vXq0Yvbn1ik0wUGgwKxZ0bRWGO45JblEJB1WSFg5yLOZ/CyFPDNbhxuUxf0T2vTGiaWX8M0qV6e6Pk2rmFTvxkndXd9Wrxf96owPT1uJQmLxCMWD2UFopiRusq6URaEKgWnnBhpf8rFTPuC0FfeF1CdDfyfTLsHEaev/NtHJMVGuQ5eUH2SURekS45IT0yIIJ8JF/ID/IzuA6+B7+C36vRteBmp03+QfDnL8j7scI=</latexit><latexit sha1_base64="jP6kyVaaI0YC4/4oQlRQprEcn2I=">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</latexit><latexit sha1_base64="fBIAPU9+eQMZvUizSiXhzPwUqcg=">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</latexit>

sin 2✓M =sin 2✓

q1� 2Losc cos 2✓

K +�LoscK

�2<latexit sha1_base64="0eucoY5IVzpNWLKwkqzM6N7UJfQ=">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</latexit><latexit sha1_base64="rbrEll99PpXfMOxOPVk5wyLnQ0k=">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</latexit><latexit sha1_base64="rbrEll99PpXfMOxOPVk5wyLnQ0k=">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</latexit><latexit sha1_base64="GY3Jp03HkbKTP+coizw6gOWsBd4=">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</latexit>

LM =Loscq

1� 2Losc cos 2✓K +

�LoscK

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K =2⇡

p2GF Ne

=1.7⇥ 107

⇢ ZA

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Riassumendo •  L’ipotesi di oscillazione del neutrino offre una elegante

soluzione al problema del neutrino solare:

I 3 problemi del neutrino solare 1)  Tutti gli esperimenti vedono un

flusso significativamente inferiore a quello previsto (1/2 o 1/3);

2)  I risultati di SuperK e Homestake sono inconsistenti fra di loro;

3) Gallex misura un flusso consistente con la sola sorgente pp (e’ quella prevista con maggiore precisione in quanto direttamente legata alla luminosita’ solare): non c’e’ spazio per gli altri tipi di neutrino;

Le soluzioni 1)  Parte dei νe oscillano in ν di altri

sapori; gli esperimenti sono “ciechi” o ”parzialmente ciechi” ai ν di altri sapori e quindi vedono un flusso minore del previsto;

2)  Homestake e’ “cieco” a νµ e ντ; SuperK invece e’ parzialmente cieco” . Inoltre vedono neutrini di energie diverse e la probabilita’ di oscillazione dipende dall’energia!

3)  La probabilita’ di oscillazione dipende dall’E; se e’ minore per basse energie i neutrini da pp sono meno soppressi degli altri;

Confronto teoria/esperimenti •  Si noti che l’ipotesi di oscillazioni nel vuoto e oscillazioni nella materia

sono in realta’ due facce della stessa medaglia: si fondano sulla stessa base teorica e dipendono (seppur in modo diverso) dagli stessi parametri: dall’angolo di mixing θ e da Δm2;

•  L’analisi combinata dei risultati degli esperimenti descritti fino ad ora, Homestake, Gallex, Sage, Kamiokande e Superkamiokande seleziona diverse regioni possibili nello spazio dei parametri θ e Δm2;

SMA Δm2=5.0x10-6eV2

sen22θ=7.2x10-3

LOW Δm2=1.0x10-7eV2

sen22θ=0.9

LMA Δm2=2.7x10-5eV2

sen22θ=0.79 Vacuum 1 Δm2=6.5x10-10eV2

sen22θ=0.79

Vacuum 2 Δm2=4.4x10-11eV2

sen22θ=0.90

I neutrini solari e da supernova (parte 1)

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