اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديد$g$-matrix folding-model approach to reaction cross sections for scattering of Ca isotopes on a C target
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We first predict the ground-state properties of Ca isotopes, using the Gogny-D1S Hartree-Fock-Bogoliubov (GHFB) with and without the angular momentum projection (AMP). We find that $^{64}$Ca is an even-dripline nucleus and $^{59}$Ca is an odd-dripline nucleus, using $A$ dependence of the one-neutron separation energy $S_{1}$ and the two-neutron separation energy, $S_{2}$. As for $S_{1}$, $S_{2}$ and the binding energies $E_{rm B}$, our results agree with the experimental data in $^{40-58}$Ca. As other ground-state properties of $^{40-60,62,64}$Ca, we predict charge, proton, neutron, matter radii, neutron skin and deformation. As for charge radii, our results are consistent with the experimental data in $^{40-52}$Ca. For $^{48}$Ca, our results on proton, neutron, matter radii agree with the experimental data. Very lately, Tanaka et. al. measured interaction cross sections for $^{42-51}$Ca scattering on a $^{12}$C target at an incident energy per nucleon of $E_{rm lab}=280$MeV. Secondly, we predict reaction cross sections $sigma_{rm R}$ for $^{40-60,62,64}$Ca, using a chiral $g$-matrix double-folding model (DFM). To show the reliability of the present DFM for $sigma_{rm R}$, we apply the DFM for the data on $^{12}$C scattering on $^{9}$Be, $^{12}$C, $^{27}$Al targets in $30 < E_{rm lab} < 400 $MeV, and show that the present DFM is good in $30 < E_{rm lab} < 100 $MeV and $250 < E_{rm lab} < 400 $MeV. For $110 < E_{rm lab} < 240 $MeV, our results have small errors. To improve the present DFM for $sigma_{rm R}$, we propose two prescriptions.
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For $^{48}$Ca, we determined $r_{m}$fm and $r_{rm skin}$fm from the central values of $sigma_{rm R}({rm EXP})$ of p+$^{48}$Ca scattering, using the chiral (Kyushu) $g$-matrix folding model with the GHFB+AMP densities. For $^{40}$Ca, Zenihiro {it et a
l.} determined $r_n({rm RCNP})=3.375$~fm and $r_{rm skin}({rm RCNP})=-0.01 pm 0.023$fm from the differential cross section and the analyzing powers for p+$^{40}$Ca scattering. For $^{40}$Ca, $sigma_{rm R}({rm EXP})$ are available with high accuracy. Our aim is to determine matter radius $r_{m}^{40}$ and skin $r_{rm skin}^{40}$ from $sigma_{rm R}({rm EXP})$ by using the Kyushu $g$-matrix folding model with the GHFB+AMP densities. We first determine $r_m({rm RCNP})=3.380$fm from the central value -0.01~fm of $r_{rm skin}({rm RCNP})$ and $r_p({rm RCNP})=3.385$fm. The folding model with the GHFB+AMP densities reproduces $sigma_{rm R}({rm EXP})$ in $30 leq E_{rm in} leq 180$MeV, in 2-$sigma$ level. We scale the GHFB+AMP densities so as to $r_p({rm AMP})=r_p({rm RCNP})$ and $r_n({rm AMP})=r_n({rm RCNP})$. The $sigma_{rm R}({rm RCNP})$ thus obtained agrees with the original one $sigma_{rm R}({rm AMP})$ for each $E_{rm in}$. For $E_{rm in}=180$MeV, we define $F$ as $F=sigma_{rm R}({rm EXP})/sigma_{rm R}({rm AMP})=0.929$. The $Fsigma_{rm R}({rm AMP})$ be much the same as the center values of $sigma_{rm R}({rm EXP})$ in $30 leq E_{rm in} leq 180$MeV. We then determine $r_{rm m}^{40}({rm EXP})$ from the center values of $sigma_{rm R}({rm EXP})$, using $sigma_{rm R}({rm EXP})=C r_{m}^{2}({rm EXP})$ with $C=r_{m}^{2}({rm AMP})/(Fsigma_{rm R}({rm AMP}))$. The $r_{m}({rm EXP})$ are averaged over $E_{rm in}$. The averaged value is $r_{m}({rm EXP})=3.380$fm. Eventually, we obtain $r_{rm skin}({rm EXP})=-0.01$fm from the averaged $r_{rm m}({rm EXP})$~fm and $r_p({rm PCNP})=3.385$fm.
In our previous paper, we predicted $r_{rm skin}$, $r_{rm p}$, $r_{rm n}$, $r_{rm m}$ for $^{40-60,62,64}$Ca after determining the neutron dripline, using the Gogny-D1S HFB (GHFB) with and without the angular momentum projection (AMP). Using the chir
al $g$-matrix folding model, we predicted $sigma_{rm R}$ for Ca scattering on a $^{12}$C target at 280 MeV/nucleon, since Tanaka {it el al.} measured interaction cross sections $sigma_{rm I} (approx sigma_{rm R})$ for $^{42-51}$Ca in RIKEN. After our prediction, they determine $r_{rm m}({rm RIKEN})$, $r_{rm skin}({rm RIKEN})$, $r_{rm n}({rm RIKEN})$. In this paper, we reanalyses the $sigma_{rm I}$, since they assumed the Wood-Saxon densities for $^{42-51}$Ca. The $sigma_{rm R}$ calculated with the folding model with GHFB and GHFB+AMP densities almost reproduce the $sigma_{rm I}$. We then scale proton and neutron densities so that $r_{rm p}$ and $r_{rm n}$ may agree with the central values of $r_{rm p}(rm exp)$ and $r_{rm n}({rm RIKEN})$, respectively. The $sigma_{rm R}$ calculated with the scaled densities do not reproduce the central values of $sigma_{rm I}$ perfectly. We then determine the $r_{rm m}$ that agree with the central values of $sigma_{rm I}$, using the chiral $g$-matrix folding model. The fitted $r_{rm m}$ do not reproduce the central values of $r_{rm m}({rm RIKEN})$ perfectly, but are in one $sigma$ level. Finally, we show the $r_{rm skin}$, $r_{rm n}$ determined from the fitted $r_{rm m}$ are close to the original ones except for $r_{rm skin}^{48}$. The fitted $r_{rm skin}^{48}$ is 0.105 fm, while the central value of $r_{rm m}^{48}({rm RIKEN})$ is 0.146 fm. When we fit $r_{rm m}$ to the upper bound of $sigma_{rm I}$, the fitted $r_{rm skin}^{48}$ is 0.164~fm and near the central vale 0.17 fm of the high-resolution $E1$ polarizability experiment.
We systematically study total reaction cross sections of carbon isotopes with N=6-16 on a proton target for wide range of incident energies, putting an emphasis on the difference from the case of a carbon target. The analysis includes the reaction cr
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Background: Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with Gogny-HFB (GHFB) with the angular momentum projection (AMP), we determined the central values of matter radius and neutron skin from the central values
of reaction cross sections $sigma_{rm R}({rm EXP})$ of p+$^{40,48}$Ca and p+$^{208}$Pb scattering. As for p+$^{58}$Ni scattering, $sigma_{rm R}({rm EXP})$ are available as a function of incident energy $E_{rm in}$. Aim: Our aim is to determine matter radius $r_{m}$ and skin $r_{rm skin}$ for $^{58}$Ni from the $sigma_{rm R}({rm EXP})$ of p+$^{58}$Ni scattering by using the Kyushu $g$-matrix folding model with the GHFB+AMP densities. Results: For p+$^{58}$Ni scattering, the Kyushu $g$-matrix folding model with the GHFB+AMP densities reproduces $sigma_{rm R}({rm EXP})$ in $8.8 leq E_{rm in} leq 81$MeV. For $E_{rm in}=81$MeV, we define the factor $F$ as $F=sigma_{rm R}({rm EXP})/sigma_{rm R}({rm AMP})=0.9775$. The $Fsigma_{rm R}({rm AMP})$ be much the same as the center values of $sigma_{rm R}({rm EXP})$ in $8.8 leq E_{rm in} leq 81$MeV. We then determine $r_{rm m}({rm EXP})$ from the center values of $sigma_{rm R}({rm EXP})$, using $sigma_{rm R}({rm EXP})=C r_{m}^{2}({rm EXP})$ with $C=r_{m}^{2}({rm AMP})/ (Fsigma_{rm R}({rm AMP}))$. The $r_{m}({rm EXP})$ thus obtained are averaged over $E_{rm in}$. The averaged value is $r_{m}({rm EXP})=3.697$fm. Eventually, we obtain $r_{rm skin}({rm EXP})=0.023$fm from $r_{rm m}=3.697$fm and $r_p({rm EXP})=3.685$fm of electron scattering.
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