Production cross sections from ${}^{82}$Se fragmentation as indications of shell effects in neutron-rich isotopes close to the drip-line

Production cross sections for neutron-rich nuclei from the fragmentation of a ${}^{82}$Se beam at 139 MeV/u were measured. The longitudinal momentum distributions of 126 neutron-rich isotopes of elements $11\le Z\le 32$ were scanned using an experimental approach of varying the target thickness. Production cross sections with beryllium and tungsten targets were determined for a large number of nuclei including several isotopes first observed in this work. These are the most neutron-rich nuclides of the elements $22\le Z\le 25$ (${}^{64}$Ti, ${}^{67}$V, ${}^{69}$Cr, and ${}^{72}$Mn). One event was registered consistent with ${}^{70}$Cr and another one with ${}^{75}$Fe. The production cross sections are correlated with $Q_g$ systematics to reveal trends in the data. The results presented here confirm our previous results from a similar measurement using a ${}^{76}$Ge beam and can be explained with a shell model that predicts a subshell closure at $N=34$ around $Z=20$. This is demonstrated by systematic trends and calculations with the abrasion-ablation model that are sensitive to separation energies.

Figure 1

The region of the nuclear chart investigated in the present work. The solid line shows the limit of bound nuclei from the KTUY mass model [7]. The new isotopes observed for the first time in the present work are marked by red squares.

Figure 2

Particle identification plot showing the measured atomic number $Z$ versus the calculated function $A-3Z$ for the nuclei observed in production runs of this work. See text for details. The limit of previously observed nuclei is shown by the solid red line, and the location of ${}^{64}$Ti is marked.

Figure 3

Mass spectra of the elements $21\le Z\le 26$ that were stopped in the Si telescope during the production runs. The limits of previously observed nuclei are shown by the vertical dashed lines. Standard deviations produced with the Gaussian function at constant width (dashed curves) are given in the panel figures for each element.

Figure 4

Differential cross sections of ${}^{66}$Fe fragments obtained by varying the target thickness with the analysis line set at one fixed magnetic rigidity. The dashed line represents the fitted asymmetric Gaussian function. Blue horizontal errors with diamonds in the center correspond to the velocity difference caused by production at the beginning or the end of target, whereas the red circles show the position of the most probable velocity based on the momentum distribution parametrization.

Figure 5

Widths of the parallel momentum component as a function of the mass number of fragments produced in the reaction ${}^{82}$Se beams with beryllium targets. Small diamonds denote calculations by the convolution model [38] with default settings for separation energy ($E_s$) option #1 in lise${}^{++}$. Solid green and dot-dashed black lines represent the best fit to the data for the Goldhaber [35] and Morrissey [36] models, respectively.

Figure 6

Inclusive production cross sections for fragments from the reaction of ${}^{82}$Se with beryllium and tungsten targets shown as a function of the mass number. The cross sections with the beryllium targets derived by momentum distribution integration are shown by stars, and those normalized with lise${}^{++}$ transmission calculations are indicated by solid diamonds. The cross sections obtained with the tungsten target were normalized with lise${}^{++}$ transmission calculations. The red solid lines show the predictions of the epax3 systematics [40] for beryllium (see text). The two magenta dashed lines separate nuclei that require neutron pickup in the production mechanism.

Figure 7

Measured cross sections versus $-Q_g$ for the production of neutron-rich calcium (top panel) and potassium (middle panel) isotopes from reactions of ${}^{82}$Se and ${}^{76}$Ge with a beryllium target. Production cross sections of sulfur and titanium isotopes from the reaction of ${}^{82}$Se with a beryllium target are shown in the bottom panel. See text for explanation of $Q_g$ and the lines. Neutron numbers of isotopes are shown in the figure. A horizontal dashed green line in the top panel shows the cross-section limit reached in the experiment with the ${}^{82}$Se beam.

Figure 8

The two-neutron separation energy $S_{2n}$ deduced from mass values as a function of the neutron number for calcium (top), potassium (middle), and sulfur and titanium isotopes (bottom). Those from experimental mass values [42] are shown by diamonds and those from AME2012 [43] by crossed circles. Results based on the full $pf$-shell phenomenological GXPF1B5 [29] interaction and the KTYU mass model [7] are shown by solid squares and empty triangles, respectively. Arrows show regions of isotopes whose measured cross sections are shown in Fig. 7.

Figure 9

Production cross section versus atomic number ($Z$) for fragments from the reaction of ${}^{82}$Se with beryllium targets. Lines are connected according to constant $N-2Z$, while labels represent the neutron number. Reactions resulting in neutron pickup are omitted. The red dashed quadrangle is explained in the text.

Figure 10

Two-neutron separation energy ($S_{2n}$) versus neutron number ($N$) for elements $12\le Z\le 22$. Values are calculated using results from the GXPF1B5 [29] model. Labels in the lines show the atomic numbers of the nuclei. The red dashed quadrangle is explained in the text.

Figure 11

Top: The cross section versus neutron number for the production of neutron-rich potassium (left) and calcium (right) isotopes from the reaction of ${}^{82}$Se on beryllium targets. The measured values are shown by semisolid rectangles. The results from the abrasion-ablation calculations using the masses obtained via both the GXPF1B and GXPF1B5 interactions [29] are shown by open diamonds with dashed lines and solid lines, respectively. For comparison, the values obtained from the epax3 systematics [40] (small solid rectangles with dashed-dot-dot lines) are also included. Bottom: Logarithm ratios of calculated and experimental cross sections shown for clearer presentation differences between experimental and calculated values. This presentation includes results from the KTYU model [7] (solid triangles with dotted lines) and the AME2012 table [43] (semisolid circles with dash-dotted lines).