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تسجيل مستخدم جديدElectric dipole polarizability of $^{48}$Ca and implications for the neutron skin
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J. Birkhan
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The electric dipole strength distribution in Ca-48 between 5 and 25 MeV has been determined at RCNP, Osaka, from proton inelastic scattering experiments at forward angles. Combined with photoabsorption data at higher excitation energy, this enables for the first time the extraction of the electric dipole polarizability alpha_D(Ca-48) = 2.07(22) fm^3. Remarkably, the dipole response of Ca-48 is found to be very similar to that of Ca-40, consistent with a small neutron skin in Ca-48. The experimental results are in good agreement with ab initio calculations based on chiral effective field theory interactions and with state-of-the-art density-functional calculations, implying a neutron skin in Ca-48 of 0.14 - 0.20 fm.
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A benchmark experiment on 208Pb shows that polarized proton inelastic scattering at very forward angles including 0{deg} is a powerful tool for high-resolution studies of electric dipole (E1) and spin magnetic dipole (M1) modes in nuclei over a broad
excitation energy range to test up-to-date nuclear models. The extracted E1 polarizability leads to a neutron skin thickness r_skin = 0.156+0.025-0.021 fm in 208Pb derived within a mean-field model [Phys. Rev. C 81, 051303 (2010)], thereby constraining the symmetry energy and its density dependence, relevant to the description of neutron stars.
{bf Background:} Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with GHFB+AMP, we determined $r_{rm skin}^{208}=0.25$fm from the central values of $sigma_{rm R}$ of p+$^{208}$Pb scattering in $E_{rm in}=40-81$MeV. Th
e high-resolution $E1$ polarizability experiment ($E1$pE) yields $r_{rm skin}^{48}(E1{rm pE}) =0.14-0.20$fm. The data on $sigma_{rm R}$ are available as a function of $E_{rm in}$ for $p$+$^{48}$Ca scattering. {bf Aim:} Our aim is to determine $r_{rm skin}^{48}$ from the central values of $sigma_{rm R}$ for $p$+$^{48}$Ca scattering by using the folding model. {bf Results:} As for $^{48}$Ca, we determine $r_n(E1{rm pE})=3.56$fm from the central value 0.17fm of $r_{rm skin}^{48}(E1{rm pE})$ and $r_p({rm EXP})=3.385$fm of electron scattering, and evaluate $r_m(E1{rm pE})=3.485$fm from the $r_n(E1{rm pE})$ and the $r_p({rm EXP})$ of electron scattering. The folding model with GHFB+AMP densities reproduces $sigma_{rm R}$ in $23 leq E_{rm in} leq 25.3$ MeV in one-$sigma$ level, but slightly overestimates the central values of $sigma_{rm R}$ there. In $23 leq E_{rm in} leq 25.3$MeV, the small deviation allows us to scale the GHFB+AMP densities to the central values of $r_p({rm EXP})$ and $r_n(E1{rm pE})$. The $sigma_{rm R}(E1{rm pE})$ obtained with the scaled densities almost reproduce the central values of $sigma_{rm R}$ when $E_{rm in}=23-25.3$MeV, so that the $sigma_{rm R}({rm GHFB+AMP})$ and the $sigma_{rm R}(E1{rm pE})$ are in 1-$sigma$ of $sigma_{rm R}$ there. In $E_{rm in}=23-25.3$MeV, we determine the $r_{m}({rm EXP})$ from the central values of $sigma_{rm R}$ and take the average for the $r_{m}({rm EXP})$. The averaged value is $r_{m}({rm EXP})=3.471$fm. Eventually, we obtain $r_{rm skin}^{48}({rm EXP})=0.146$fm from $r_{m}({rm EXP})=3.471$fm and $r_p({rm EXP})=3.385$fm.
[Background]: 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 with and without the angular momentum projection (AMP). We foun
d that effects of the AMP are small. Very lately, Tanaka {it et al.} measured interaction cross sections $sigma_{rm I}$ for $^{42-51}$Ca, determined $r_{rm m}$ from the $sigma_{rm I}$, and deduced skin $r_{rm skin}$ and $r_{rm n}$ from the $r_{rm m}$ and the $r_{rm p}(rm {exp})$ evaluated from the electron scattering. Comparing our results with the data, we find for $^{42-48}$Ca that GHFB and GHFB+AMP reproduce the data on $r_{rm skin}$, $r_{rm n}$, $r_{rm m}$, but not for $r_{rm p}(rm {exp})$. [Aim]: Our purpose is to determine a value of $r_{rm skin}^{48}$ by using GHFB+AMP and the constrained GHFB (cGHFB) in which the calculated value is fitted to $r_{rm p}(rm {exp})$. [Results]: For $^{42,44,46,48}$Ca, cGHFB hardly changes $r_{rm skin}$, $r_{rm m}$, $r_{rm n}$ calculated with GHFB+AMP, except for $r_{rm skin}^{48}$. For $r_{rm skin}^{48}$, the cGHFB result is $r_{rm skin}^{48}=0.190$fm, while $r_{rm skin}^{48}=0.159$fm for GHFB+AMP. We should take the upper and the lower bound of GHFB+AMP and cGHFB. The result $r_{rm skin}^{48}=0.159-0.190$fm consists with the $r_{rm skin}^{48}(sigma_{rm I})$ and the data $r_{rm skin}^{48}(rm $E1$pE)$ obtained from high-resolution $E1$ polarizability experiment ($E1$pE). Using the $r_{rm skin}^{48}$-$r_{rm skin}^{208}$ relation with strong correlation of Ref.[3], we transform the data $r_{rm skin}^{208}$ determined by PREX and $E1$pE to the corresponding values, $r_{rm skin}^{48}(rm tPREX)$ and $r_{rm skin}^{48}(rm t$E1$pE)$. Our result is consistent also for $r_{rm skin}^{48}(rm tPREX)$ and $r_{rm skin}^{48}(rm t$E1$pE)$.
For a bound state internal wave function respecting parity symmetry, it can be rigorously argued that the mean electric dipole moment must be strictly zero. Thus, both the neutron, viewed as a bound state of three quarks, and the water molecule, view
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