bounds to binding energies from concavity
DESCRIPTION
Bounds to Binding Energies from Concavity. N.P. Toberg Dr. B.R. Barrett Department of Physics, University of Arizona, Tucson Az 85721 USA Dr. B.G. Giraud Service de Physique Th éorique, DSM, CE Saclay, F-911191 Gif/Yvette, France. 1) INTRODUCTION. - PowerPoint PPT PresentationTRANSCRIPT
Bounds to Binding Energies from Concavity
N.P. TobergDr. B.R. BarrettDepartment of Physics,
University of Arizona, Tucson Az 85721 USADr. B.G. Giraud
Service de Physique Théorique,DSM, CE Saclay, F-911191 Gif/Yvette, France
1) INTRODUCTION
• Search for 1st order approximation to isotope binding energy (Upper and Lower Bounds)
• Exploit properties of the quadratic terms in nuclear binding energy formula
3) IntroductionComplete Binding Energy
Krane, Kenneth. Introductory Nuclear Physics. John Wiley & Sons, Inc., 1988.
AZAaAZZaAaAaB symcsv
23/13/2 )2()1(
NZA
4) Introduction
i. Dominant terms define a paraboloid energy surface (concave)
ii. Deviations from concavity can be suppressed ( )
iii. This work done in the zero temperature limit
),(,),(,3/2 ZNpZNsA
5) Methods
• Choose a sequence of isotopic energies
• To first approximation, assume the equality of differences in neighboring isotope energies:
121 AAAA EEEE
SnSnSnEEEor 1131151142:
6) Sn Staggering from 1st Differences
7)Methods
• To estimate curvature, look at second differences :
• This is analogous to taking the second derivative of the energy with respect to the atomic number A.
11 2
AAA EEEAE
8) Methods (Result of Second Differences for Sn)
9)Methods
• Second Differences showcase alternating signs due to pairing effects from even isotopes.
• We suppress pairing by looking at the general trend and adding an appropriate constant energy to each even isotope. This will affect each number in SD’s.
10) Methods (pairing suppression for Sn)
Data after pairing correction
11) Methods
• After p(N,Z) is corrected, a parabolic correction is imposed on each Second Difference.
2)(2 middlenegativemost AA
E
12) Results (Sn)
Bare Data
Pairing Correction (full line)
Parabolic Correction (dashed line)
Second Differences 11 2 AAA EEE
13) Results (Pb)
14) Methods
Sn isotope bindings, irregular line joins bare data;pairing and parabolic corrections give non-connecteddots.
15) Methods (Results for Lead Isotopes)
16) Goal
• Using a simple approximation in 1st order nuclear theory, quickly obtain upper or lower bounds for unknown isotopic energies.
17) Required Parameters
1. Sequence of known isotopic energies surrounding unknown values
2. Empirical value to suppress pairing3. Most negative value after Second
Differences are obtained
18)Results
• Extrapolations
• Interpolations
212 AAA EEE
221
AAA
EEE
19) Extrapolations &Interpolations:
Sn117
Uncorrected Data Corrected DataB.E
A
B.E.
A
20)Results from Interpolation For
Uncorrected (keV) Error (Underbinding)
-996816 1191
Corrected (keV) Error (Underbinding)
-995466 159
Sn117
21)Results for Extrapolation of Sn117
Uncorrected (keV) (From higher masses) Error (Overbinding)-998467 2842
Corrected (keV) Error (Overbinding)-996967 1342
Uncorrected (keV) (From lower masses) Error (Overbinding)-998243 2618
Corrected (keV) Error (Overbinding)-996743 1118
22)Extrapolations for Ground State Energy of = -934562 keV
Uncorrected (keV) Error (keV)-931957 2605
Corrected (keV) Error (keV)-934657 95
Sn110
23)Results
• Extrapolation for with uncorrected data gives an over-binding of keV
• The same extrapolation for with corrected data gives an over-binding of keV
Pb179
Pb179
keVEPb
3101378179 3103
3101
24) Conclusions• Future work is needed to expand this technique for both
N & Z as variables
• Development of algorithms to quickly process energy sequences is in development
• High temperature limit gives estimates of partition functions
• Predicative ability greatly enhanced by introducing pairing suppression and by favoring of parabolic terms in binding energy formula
Acknowledgements
• Dr. Bruce Barrett
• Dr. Alex Lisetsky