T. R. Routray School of Physics Sambalpur …...The total nuclear direct and exchange energy density...
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T. R. Routray School of Physics Sambalpur University, Jyotivihar, Burla, India 1
Transcript of T. R. Routray School of Physics Sambalpur …...The total nuclear direct and exchange energy density...
T. R. Routray School of Physics
Sambalpur University, Jyotivihar, Burla, India
1
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YUKAWA GAUSSIAN
-129.247 -96.2443
α (fm) 0.42316 0.75766
9
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00 0
fmMeVTMeVe f
J.Phys. G: Nucl. Part. 24 (1998) 2073
0),( 0300 ku
and Ʌ - determined simultaneously using an optimisation procedure
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𝑚∗
𝑚(k=𝑘𝑓0
,ρ0) 0.686 0.709
𝑚∗
𝑚(k=0,ρ0) 0.609 0.660
𝑢 (k=∞,ρ0)MeV 35.89 12.68 𝑢 (k=0,ρ0) MeV -73.11 -70.05 𝑢𝑅(ρ0) MeV
15.93 16.91
11
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l0
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123
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12
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13
Danielewicz P et al., Science 298 (2002) 1592
into two specific channels for interactions between like (l) and
unlike (ul) nucleons.
The sign of (εex
l – ε
ex
ul) splitting of n and p effective masses.
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15
Hodgson P E, 1994 The Nucleon Optical Model (Singapore: World Scientific, p613
Entropy Density
Behera et al. JPG 38 (2011) 115104
,)(1ln)(1)(ln)()2(
),( 3,0,0,0,0
3
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n
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n
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l
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,),(k,
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F. Sammurraca, Int. J. Mod. Phys. E 19 (2010) 1259
17
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d
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YPYPYPYP
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),(),(),(),(
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18
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2
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Behera et al., JPG 36 (2009) 125105
Same density dependence of the EOS in ANM for widely varying momentum dependence of the mean field and vice versa; Therefore, the simple effective interaction can be used in the transport model analysis of the flow data.
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• 09-parameters of ANM three standard
values e(ρ0), ρ0 and 𝐸𝑠(ρ0) for a given γ.
• Out of 11-interaction parameters, two parameters open. We have taken
𝑡0 and 𝑥0
as the open parameters.
• We further constrain one more parameter, namely, 𝑥0
from spin polarization property in NM.
Spin polarized Neutron Matter
21 ,
2
)( ,, ull
ex
ll
exl
ex
,
2
)( ,, ullll
l
2
)( ,
0
,
00
ulllll
pdnu
ndnu
ndnu
ndnu
ndnu
ndnu
,),(k,m
*m),(k,
m
*m
k
),(k,u
k
m1),(k,
m
*m1
ndnu,
2
,
Only one parameter 𝒕𝟎 kept open which shall be determined from finite nucleus.
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ll
ex
l
ex
l
tx ,
0
00
02
321
rdrfV TOll
ex
3
00
, )(
)034315200775( PRCKrastevGPandSammarrucaF
predictionDBHFwithagreement
l
ex
ull
ex
ll
ex 2)( ,,
l
ex
ll
ex 3
1,
FINITE NUCLEI
The many-body Hamiltonian with an effective interaction
Kinetic Energy Finite range + spin-orbit
Coulomb Interaction
Again,
Simple effective Interaction
Spin-orbit Interaction
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The total nuclear direct and exchange energy density coming from SEI. The non-local exchange part is made local by using semi-classical ħ-expansion of density matrix upto 2nd order. (X.Viñas et. al. PRC 67 (2003) 014324)
The Spin-orbit interaction taken similar to Skyrme and Gogny interaction.
𝒕𝟎 𝑪𝒂40 𝑾𝟎(strength parameter of Spin-orbit interaction)
𝑃𝑏 208 BEs of 161 - and Radii of 86- spherical nuclei: A=16 to A=224 24
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𝛿𝐸 𝑟𝑚𝑠=1.70 MeV
𝛿𝐸 𝑟𝑚𝑠=1.68 MeV
𝛿𝐸 𝑟𝑚𝑠=1.85 MeV
𝛿𝐸 𝑟𝑚𝑠=1.83 MeV
2
exp
2 )(1
)( tcalcrms EEN
E)( exptcalc EEE
6/1
3/1
2/1
3/2
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𝛿𝑟 𝑟𝑚𝑠=0.0189
𝛿𝑟 𝑟𝑚𝑠=0.0170
𝛿𝑟 𝑟𝑚𝑠=0.0155
𝛿𝑟 𝑟𝑚𝑠=0.0152
2
exp
2 )(1
)( tcalcrms rrN
r)( exptcalcch rrr
6/1
3/1
2/1
3/2
27
28 Behera et. al., J.Phys G (2013) 095105; (2015) 045103
𝛾=1/3 𝑡0=201, 𝑊0=115 ∆𝐸𝑟𝑚𝑠=1.873(HFB) 𝑡0=214, 𝑊0=115 ∆𝐸𝑟𝑚𝑠=1.788 (EROT)
𝛾 =1/2 𝑡0=438, 𝑊0=112 ∆𝐸𝑟𝑚𝑠=1.958 (HFB) 𝑡0=450, 𝑊0=115 ∆𝐸𝑟𝑚𝑠=1.843 (EROT)
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HFB results with SEI for 579 even-even nuclei, deformed and spherical, over the nuclear chart
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CONCLUSION:
• By adjusting the parameters of SEI from considerations of momentum dependence of the mean fields in NM, the interaction could predict the finite nuclei properties similar in quality as that of any other conventional interaction.
• The procedure of parameter fixation provide the flexibility of
systematically varying the momentum dependent properties, where the EOSs remains the same and vice-versa.
• The preliminary results of HFB with SEI shows that it is also
competent to account for the deformation properties in finite nuclei similar in quality as any other successful effective interaction.
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• Collaborators
B.Behera, Sambalpur University, India
X.Viñas, University of Barcelona, Spain
M. Centelles, University of Barcelona, Spain
L. Robledo, University of Madrid, Spain
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THANK YOU
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