1. Assistant professor at Isfahan University of Technology, Isfahan, Iran
ECT* DOCTORAL TRAINING PROGRAM
Nucleon-Nucleon correlation and distribution functions in the LOCV approximation
Azar Tafrihi
Assistant professor at Isfahan University of Technology, Isfahan, Iran
A. Tafrihi, ECT* 2017, 1

2. OUTLINE INTRODUCTION: The av18 potential THE LOCV APPROXIMATION
THE LOCV CORRELATION FUNCTIONS
THE LOCV DISTRIBUTION FUNCTIONS
SUMMARY & OUTLOOK
A. Tafrihi, ECT* 2017, 1

3. AV18 INTERACTION Charge dependent Charge asymmetric
R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev. C 51, 38, 1995.
A. Tafrihi, ECT* 2017, 1

4. ECT* DOCTORAL TRAINING PROGRAM
The LOWEST ORDER CONSTRAINED VARIATIONAL (LOCV) APPROXIMATION
M. Modarres, A. Tafrihi, Nucl. Phys. A, 879, 1 (2012).

5. APPROXIMATION THE LOWEST ORDER CONSTRAINED VARIATIONAL (LOCV)
The LOCV method is a variational approach
We look for the upper bound to the ground state energy
The energy is minimized respected to the variational wave function
The energy could be expanded in the number of A-body clusters:
In the LOCV approx. the expansion is truncated at the two-body cluster.
In the Extended LOCV the expansion is truncated at the three-body cluster.
3D integrations

6. THE LOCV FORMALISIM FOR A CENTRAL POTENTIAL

7. THE LOCV EULER-LAGRANGE EQUATION

8. ECT* DOCTORAL TRAINING PROGRAM
The LOCV correlation functions
M. Modarres, A. Tafrihi, Nucl. Phys. A 941, 212 (2015).

9. The E-L equation is solved in each channel
THE LOCV NUCLEON-NUCLEON CORRELATION FUNCTIONS
ST=00,01,10,11
The E-L equation is solved in each channel

10. THE LOCV SNM CF VS. THOSE OF FHNC (AV18)
Generally the behavior of the LOCV predictions agrees with those FHNC
Although there are some disagreements
Disagreements refer to the many-body effects as well as three-body interaction which were considered in the FHNC calculations.
As it was expected by increasing the density the range of correlation functions reduced
The (non-)central correlations go to (0) 1 at large inter-particle distances.
0.24
0.16
A. Mukherjee, Phys. Rev. C 79 (2009)

11. ECT* DOCTORAL TRAINING PROGRAM
The LOCV distribution functions
M. Modarres, A. Tafrihi, Nucl. Phys. A 941, 212 (2015).

12. THE LOCV NUCLEON-NUCLEON DISTRIBUTION FUNCTIONS
The AV18 potential is expanded as follows:
The expectation value of the given potential can be obtained using DFs:
The central DFs gives the probability of finding two nucleons at the relative distance r.
The non-central DFs give the probability of finding non-central correlated nucleons at the relative distance r .

13. THE LOCV NUCLEON-NUCLEON DISTRIBUTION FUNCTIONS

14. THE LOCV SNM DFS VS. THOSE FHNC
The overall behavior of the LOCV computations agree with those of FHNC.
Expectedly, the LOCV results differ from those of FHNC.
By increasing the density the range of the correlations reduces.
Nucleons are dominantly correlated in:
S=0 channel.
T=0 state.
ST=01,10 states but not in ST=00,11 states.
Nucleons are dominantly tensor dependent in T=0 state but not in T=1 channel.
Nucleons are dominantly spin-orbit dependent in T=1 state but not in T=0 state.
A. Akmal, V.R. Pandharipande, Physical Review C, 56 (1997)

15. THE LOCV NM DFS VS. THOSE OF MC at 0.16 fm^-3
IN THE 3S2-3P2 COUPLED CHANNEL:
SPIN-ORBIT CORRELATION (MT1)
TENSOR CORRELATION (MT2) *5
The overall behavior of the LOCV computations agree with those of FHNC.
Expectedly, the LOCV results differ from those of FHNC.
By increasing the density the range of the correlations reduces.
The (non-)central correlations go to (0) 1. MC
J. Carlson et al., Physical Review C, 68 (2003)

16. SUMMARY
The approximated LOCV results fairly agree with those of complicated FHNC and MC methods. Because the LOCV correlation functions are special functions which satisfy the normalization constraint. So, we can ignore the contribution of higher cluster terms included in the other approaches.
An LOCV nucleonic matter calculation with the Av18 interaction, for a given density, takes a few seconds CPU time on 1.8 GHz personal computer. While, including the spin–orbit-dependent correlations, the MC calculations take more computational cost. As it was indicated above, these MC computations are expensive.
In the present paper, the spin–orbit and the tensor-dependent correlation functions are employed in the 3S1–3D1 and the 3P2–3F2 channels, respectively. So, we show that the inclusion of the spin–orbit-dependent correlation functions do not make the LOCV formalism sophisticated. Even, we illustrate that the LOCV Euler–Lagrange equations become simpler for the spin–orbit-dependent correlations in comparison with those of tensor-dependent ones. While, as it was stated above, by considering the spin–orbit correlations, the MC and the FHNC/SOC calculations become complicated. So, unavoidably, the spin–orbit correlations have been neglected in the mentioned approaches.
As it was expressed above, the MC approach has problem with the calculation of the spin–orbit-dependent distribution function. Whereas, we demonstrate that the LOCV approach is capable of calculating the spin–orbit-dependent distribution functions in a JSTTz-dependent formalism. It should be mentioned that the spin–orbit-dependent distribution functions have not yet been reported by the FHNC/SOC method. 16

17. !THANKS