Background: In our previous paper, we predicted neutron skin rskin and proton, neutron, matter radii, rp, rn, rm for 40−60,62,64Ca after determining the neutron dripline, using the Gogny-D1S Hartree-Fock-Bogoliubov (GHFB) with and without the angular momentum projection (AMP). We found that effects of the AMP are small. Very lately, Tanaka et al. measured interaction cross sections σI for 42−51Ca, determined matter radii rm(σI) from the σI, and deduced skin rskin(σI) and rn(σI) from the rm(σI) and the rp(exp) evaluated from the electron scattering. Comparing our results with the data, we find for 42−48Ca that GHFB and GHFB+AMP reproduce rskin(σI), rn(σI), rm(σI), but not for rp(exp). Aim: Our purpose is to determine a value of rskin48 by using GHFB+AMP and the constrained GHFB (cGHFB) in which the calculated value is fitted to rp(exp). Results: For 42,44,46,48Ca, cGHFB hardly changes rskin, rm, rn calculated with GHFB+AMP, except for rskin48. For rskin48 , the cGHFB result is rskin48 = 0.190 fm, while rskin48 = 0.159 fm for GHFB+AMP. We should take the upper and the lower bound of GHFB+AMP and cGHFB. The result rskin48 = 0.159 − 0.190 fm consists with the rskin48 (σI) and the data rskin48 (E1pE) obtained from high-resolution E1 polarizability experiment (E1pE). Using the rskin48 -rskin208 relation with strong correlation of Ref. , we transform the data rskin208 determined by PREX and E1pE to the corresponding values, rskin48 (tPREX) and rskin48 (tE1pE), where the symbol 't' stands for the transformed data. Our result is consistent also for rskin48 (tPREX) and rskin48 (tE1pE). Eventually, for 42,44,46,48Ca, cGHFB reproduces rskin(σI), rm(σI), rn(σI), rp(exp), while GHFB+AMP does rskin(σI), rm(σI), rn(σI).
|Publication status||Published - May 27 2020|
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