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HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M...
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Transcript of HOW TO DRAW A LEVEL SCHEME ? or ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA N. NICA TEXAS A&M...
HOW TO DRAW A LEVEL SCHEME ?or
ABOUT THE NATURE OF GAMMA-RAY SPECTROSCOPY DATA
N. NICA
TEXAS A&M UNIVERSITY
? ? ?
Concept: Data Evaluation - Rearguard of Research
• ENSDF-NDS data evaluation (sponsor: NNDC)
• Quantitative improvement of data through ICC precise measurement (sponsor: Texas A&M University)
• Qualitative reassessment of significance in γ-ray spectroscopy data (measurement & data research; sponsor: HOBBY)
Level Schemes
171Yb 155Er
Moments of Inertia 1. Collective rotations – “I(I+1) rule” directly – generating rotational bands based on particular intrinsic configurations (band heads)
)1(2
)(2
IIIE
where is the moment of inertia of the deformed core of nuclei in between closed shells , and I is the (total) nuclear spin
iRI
R is the angular momentum of the rotating core
i is the intrinsic single-particle angular momentum 2. Non-collective rotations – of spherical nuclei at closed shells, where the nuclear spin results from successive single-particle alignments and the “I(I+1) rule” is satisfied “on average”
Moments of Inertia: Band ( band ) and Effective ( eff ) Collective Non-collective
Consequences of “I(I+1)” Rule
E2 γ-ray energy:
)12(2)24(2
)2()(2
IcIIEIEE
Rotational parameter:
2
2c
γ-ray energy difference
cIEIEE 82
8)2()(2
Coincidence Matrix
Coincidence Matrix
E2
E1 E1
E2
Repeatability 1: Study of distributions of differences of γ-ray coincidence energies REPEATABILITY: - Repeated appearance of satellite peaks relative to the coincidence peaks of a reference rotational band at same location.
- The repeatability peaks are situated on a regular grid with characteristic distance dgrid:
ZnmdndmEEEE
EE
gridgridssrr
,),,(),(),(
),(
2121
21
- The repeatability peaks appears “statistically” at a number of repeatability positions, including the windows situated on the diagonal of the central valley.
Sample of repeatability around reference band [541]1/2- of 163Tm Repeatable satellite peaks on the regular grid with dgrid = 3.2 keV
EDistribution Repeatability Non-repeatability
Proj
ectio
n
Proj
ectio
n
Distribution of distances D(dist) ofEdistribution
Repeatability Non-repeatability
Projection of
D(dist)
E distribution
543210
125
100
75
50
25
125
100
75
50
25
543210
1 2 3 40 E(keV)
1 2 3 40
1 2 3 40 (keV)E
(keV) 1 2 3 40-1-2-3-4 -1-2-3-4-1-2-3-4 (keV)
Cou
nts
Cou
nts
Cou
nts
Cou
nts
Repeatability of [411]1/2+ band in 163Tm
ΔEγ from upper half of coinc. matrix (case “I”): dgrid = 4.5 keV
Distributions D(dist): dgrid = 4.5 keV IMP!: Fractal-like structure of hierarchized maxima!
Repeatability of [541]1/2- band in 163Tm DS(dist) distribution Dgrid = 0.8 keV
Repeatability in 163Tm (all-bands reference, “total reference”)
ΔEγ distribution (1 kev/ch) reveal large scale repeatability pattern with dgrid ≈ 2.7 keV
Detail of same ΔEγ distribution (0.1 kev/ch – default value)
Repeatability in 163Tm (all-bands reference) – cont.
DR(dist) for the detail of ΔEγ (previous figure), revealing oscillations around plateau
Repeatability pattern with dgrid ≈ 2.65 keV
Repeatability in 162Tm (all-bands reference)
ΔEγ distribution of type “R” (black points, superposed with their fit with 2D spline functions)
DR(dist) revealing repeatability pattern with dgrid ≈ 3.4 keV
Repeatability in 168Yb (all-bands reference)
ΔEγ distribution of type “S”
DS(dist) revealing repeatability pattern with dgrid ≈ 3.0 keV
Repeatability findings
Nucleus Dgrid (keV) / Ref. type Obs. 163Tm odd
2.65 (total)
4.5 ([411]1/2+)
0.8 ([541]1/2-)
2.65 = (4.5+0.8)/2
162Tm odd-odd
3.4 (total)
168Yb even-even
3.0 (total)
Repeatability: -Regular & Symmetrical Grid of repeated satellite peaks -Everywhere in the coincidence matrix including central valley -Structure of Recursively-Hierarchized Maxima “fractal-like”
ΔEγ Differential Distributions
-10:10 keV, 0.1 keV/ch -50:50 keV, 1 keV/ch -200:200 keV, 40 keV/ch
Repeatability is an Overabundant Property:• Affecting the bulk of data• Sampled manifold repeatability experimental coincidence data
and published data level schemes• It is not outstanding or astounding• Can not be seen in 1D gate spectra• It is dissimulated in 2D coincidence data• Observance & understanding are gradual and cumulative• It is the “tissue” rotational structures are made of• General property that can not be reduced to known phenomena• Does not contradict but include known physics
REPEATABILITY IS THE TRUE NATURE OF GAMMA-RAY SPECTROSCOPY DATA
Consequences on levels schemes
Comparison of Fluctuation Analysis Method (FAM)
and ΔEγ Distribution Method (2DΔEγ)
FAM 2D ΔEγ
- Macroscopic-microscopic paradigm (order-random) :
- Macro = liquid drop = order = “8c” effective rotor periodic ridges distance
- Micro = quantum shell = randomness = ridges dispersion
- LS: Juxtaposition of single rotational bands
- Deformed potential - Classical-Quantum- Clumsy & non-visual sense- Data: Exclusive & Linear- Passive Data & Active Theory
- Complete recursive order paradigm (fractal-like order-order-order…):
- Regular(0) “8c” distances
- Regular(i), i=1,2,…(?) shorter distances (modulo repeatability)
- LS: Complete tissue-integrated rotational structures
- Geometry of recursive scales- Geometry <=> Relativity (?)- Beauty & restored visual sense- Data: Inclusive & Correlative- Balanced Data & Theory
GOD PLAY DICE GOD DOES NOT PLAY DICE
Conclusion• Repeatability is the true nature of the nuclear
spectroscopy data• Allowing a full decomposability “modulo
repeatability” of the data• Showing a general recursive inter-level (inter-
band) correlation property • Leading to a fully correlated structure of levels• Including non-contradictorily the known nuclear
rotation phenomena• And restoring a sense of visuability to the
quantum level of nuclear structure