Evolution of nuclear charge radii in copper and indium isotopes *

Abstract

The systematic trend in nuclear charge radii is of great interest due to the universal shell effects and odd-even staggering (OES). Modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton ($np$) correlations, is firstly applied to study the odd-$Z$ copper and indium isotopes. Theoretical results obtained by relativistic mean field (RMF) model with NL3, PK1 and NL3$^{*}$ parameter sets are compared with the experimental data. Our results show that both OES and the abrupt changes across $N=50$ and $82$ shell closures are reproduced evidently in nuclear charge radii. The inverted parabolic-like behaviors of rms charge radii can also be remarkably described between two neutron magic numbers, namely $N=28$ to $50$ for copper isotopes and $N=50$ to $82$ for indium isotopes. This implies the fact that the $np$-correlations play an indispensable role in quantitatively determining the fine structures of nuclear charge radii along odd-$Z$ isotopic chains. Meanwhile, our conclusions have almost no dependence on the effective forces.

Measurement of the diffuse gamma-ray emission from Galactic plane with LHAASO-KM2A

“…We report the measurements of the diffuse emission from the Galactic plane in a wide energy range, from 10 TeV to 1000 TeV. We use the data recorded by the square kilometer array (KM2A) of the Large High Altitude Air Shower Observatory (LHAASO) experiment located at Haizi Mountain (100 • .01E, 29 • .35N; 4400 m above the sea level), Daocheng, Sichuan province, China [24]. The LHAASO experiment is a large area, wide field-of-view observatory for CRs and γrays with hybrid detection techniques [24].…”

“…We use the data recorded by the square kilometer array (KM2A) of the Large High Altitude Air Shower Observatory (LHAASO) experiment located at Haizi Mountain (100 • .01E, 29 • .35N; 4400 m above the sea level), Daocheng, Sichuan province, China [24]. The LHAASO experiment is a large area, wide field-of-view observatory for CRs and γrays with hybrid detection techniques [24]. In April 2019, LHAASO started taking data with a partial array, and successfully opened the PeV γ-ray window with its extraordinary sensitivity [25][26][27][28][29].…”

Local variations of charge radii for nuclei with even Z from 84 to 120

“…For ease of discussion, the results obtained via equation (4) with and without considering the modified term D are denoted as RMF (BCS) * and RMF(BCS), respectively. Moreover, the abrupt changes of nuclear charge radii across shell closures can also be reproduced well [94]. The value of D is obtained by solving the state-dependent BCS equations with a zero-range δ-force interaction [60].…”

“…The RMF(BCS) * model can reproduce the shell effect in nuclear size fairly well for K, Ca, Cu, and In isotopes [74,92,94], etc, especially the inverted parabolic-like behaviors between the two closed-shells. This is an indicator of the shell effect along a long isotopic chain.…”

“…The effective force NL3 is especially favorable to the calculation of charge radii along a long isotopic chain [95]. Actually, parametrization set PK1 and NL3 * cannot change the conclusions at the quantitative level [94].…”