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Calculation of asymptotic normalization coefficients in the complex-ranged Gaussian basis

by D. A. Sailaubek, O. A. Rubtsova

Submission summary

As Contributors: Dinmukhamed Sailaubek
Arxiv Link: https://arxiv.org/abs/1910.12030v1
Date submitted: 2019-10-29
Submitted by: Sailaubek, Dinmukhamed
Submitted to: SciPost Physics Proceedings
Proceedings issue: 24th European Few Body Conference (University of Surrey, U.K.)
Discipline: Physics
Subject area: Nuclear Physics - Theory

Abstract

A new technique towards finding asymptotic normalization coefficients in the complex-ranged Gaussian basis is presented. It is shown that a diagonalisation procedure for the total Hamiltonian matrix in the given basis results in approximation for a radial part of the bound state wave function from the origin up to the far asymptotic distances, which allows to extract ANCs rather accurately. The method is illustrated by calculations of single-particle ANCs for nuclei bound states in cases of non-local nucleon-nucleus interactions, in particular, phenomenological global potentials with the Perey-Buck's non-locality.

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Editor-in-charge assigned



Reports on this Submission

Anonymous Report 1 on 2019-10-29 Invited Report

Report

Dear Editor,
in this contribution to the proceedings of the European Few-Body conference, Sailaubek and Rubtsova presents an original technique to compute the ANC of nuclear bound states described as a valence nucleon bound to a core. This method using a complex-range Gaussian basis is valid for both local an non-local interactions, which makes it particularly attractive.
The text is well written and should definitely be included within these proceedings. I have only three minor comments:
1. In (8), albeit evident, H_nn’ is not properly defined.
2. In (10), \phi_n’l should depend on (r’), I guess.
3. In the first line of Sec.3, I suggest to write: « we assume that the proton is captured by 12C in the in the 1p1/2 orbital to form the ground state of 13N. »
I assume that the proton is initially in an s continuum wave.

  • validity: high
  • significance: high
  • originality: high
  • clarity: good
  • formatting: excellent
  • grammar: good

Author Dinmukhamed Sailaubek on 2019-11-13
(in reply to Report 1 on 2019-10-29)

Dear Editors, We are grateful to the referee for useful comments and suggestions. In the new version, we made some minor corrections which are listed below. 1) According to the referee's suggestion, we have included an explicit formula for the Hamiltonian matrix prior to the eq.(8). 2) We have corrected the misprint in eq. (10) and also some other misprints throughout the text. 3) We also agree with the referee that the first sentence of Section 3 was not quite clear. It should be mentioned here that the relative momentum of the proton and 12C core is equal to 1 and the final nucleus has negative parity. Finally, we have rewritten this sentence according to the referee's suggestion.

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Comments

Dinmukhamed Sailaubek on 2019-11-13
Category:
correction

Dear Editors, We are grateful to the referee for useful comments and suggestions. In the new version, we made some minor corrections which are listed below. 1) According to the referee's suggestion, we have included an explicit formula for the Hamiltonian matrix prior to the eq.(8). 2) We have corrected the misprint in eq. (10) and also some other misprints throughout the text. 3) We also agree with the referee that the first sentence of Section 3 was not quite clear. It should be mentioned here that the relative momentum of the proton and 12C core is equal to 1 and the final nucleus has negative parity. Finally, we have rewritten this sentence according to the referee's suggestion.