High-precision mass measurements of nickel, copper, and gallium isotopes and the purported shell closure at $N=40$

High-precision mass measurements of more than 30 neutron-rich nuclides around the $Z=28$ closed proton shell were performed with the triple-trap mass spectrometer ISOLTRAP at ISOLDE/CERN to address the question of a possible neutron shell closure at $N=40$. The results for ${}^{57,60,64-69}\mathrm{Ni}$ ($Z=28$), ${}^{65-74,76}\mathrm{Cu}$ ($Z=29$), and ${}^{63-65,68-78}\mathrm{Ga}$ ($Z=31$) have a relative uncertainty of the order of ${10}^{-8}$. In particular, the mass of ${}^{76}\mathrm{Cu}$ was measured for the first time. We analyze the resulting mass surface for signs of magicity, comparing the behavior of $N=40$ with that of known magic numbers and with midshell behavior. While the classic indications from the mass surface show no evidence for a shell closure at $N=40$, there is evidence for a weak—and very localized—effect for $Z=28$, consistent with findings from nuclear spectroscopy studies.

Figure 1

Sketch of experimental setup of ISOLTRAP mass spectrometer, including the main parts: a gas-filled linear radio-frequency quadrupole (RFQ) trap for capturing and preparing the ISOLDE beam, a gas-filled cylindrical Penning trap for isobaric separation, and a hyperbolic Penning trap for the mass measurement. Microchannel plate (MCP) detectors are used to monitor the ion transfer and to measure the extracted-ion time of flight (TOF) together with the channeltron detector. Inset presents a TOF cyclotron resonance for radioactive ${}^{68}{\mathrm{Ni}}^{+}$ ions.

Figure 2

Difference between ISOLTRAP mass excess results for nickel isotopes and the AME1995 values [41]. Dashed lines represent ISOLTRAP error bars.

Figure 3

Mass excess of ${}^{69}\mathrm{Ni}$ determined by the reaction ${}^{70}\mathrm{Zn}$(${}^{14}\mathrm{C}$,${}^{15}\mathrm{O}$)${}^{69}\mathrm{Ni}$ [42], and a TOF measurement [19], the resulting AME1995 value [41], and the ISOLTRAP value. The AME2003 value [40] differs by 400 keV with an uncertainty 30 times smaller than the AME1995 value.

Figure 4

Difference between ISOLTRAP mass-excess values for copper isotopes and the 1995 AME values [41]. Dashed lines represent the ISOLTRAP error bars. $g$ denotes ground states and $m,n$ isomeric states. Mass measurements from Bai et al. [20] from 1998 are represented by open circles. ISOLTRAP improves the mass uncertainty of ${}^{72-74}\mathrm{Cu}$ over 100 times.

Figure 5

Difference between ISOLTRAP mass-excess values for gallium isotopes and the 1995 AME values [41]. Dashed lines represent the ISOLTRAP error bars.

Figure 6

Mass difference between ISOLTRAP results and model predictions for the copper isotopes. Note that ${}^{76}\mathrm{Cu}$ was measured for the first time and that the more recent parameter fit for HFB-8 included that result.

Figure 7

Difference of the nickel results from the AME2003 data which already include the present ISOLTRAP data and those predicted by HFB-D1S (Gogny) and GCM-GOA as a function of neutron number $N$ for (left) the mass and (right) the two-neutron separation energy.

Figure 8

Two-neutron separation energies ($S_{2n}$) for iron ($Z=26$) to germanium ($Z=32$) around $N=40$. Dashed lines correspond to the data before the ISOLTRAP measurements. Points with large error bars were not directly measured by ISOLTRAP but their values were changed by the link to the measured masses. Inset represents $S_{2n}^{\prime }$, which is $S_{2n}$ minus a linear function of $N$, around $N=40$.

Figure 9

Shell gap as a function of proton number $Z$ for different magic and midshell neutron numbers. $N=16,28,50,82$ correspond to shell closures; $N=39$ and 66 are exactly between two shell closures (called midshell), $N=40$ is under investigation. Data are from Ref. [40]. Inset represents a zoom for $N=38\text{–}41$.

Figure 10

(a) Pairing gap energy as a function of neutron number for the investigated elements as well as for zinc and germanium. In the case of nickel, errors above $N=41$ are too large to be relevant, so the data are not shown. (b) Pairing gap energy as a function of neutron number for $Z=27\text{–}59$. Shell closures at $N=28$, 50, and 82 are clearly visible; the $N=66$ midshell is indicated.

Figure 11

Difference between the experimental mass values from this work and from AME2003 data [40] and theoretical masses from the Bethe-Weizsäcker formula as a function of proton number, for several magic neutron numbers and for $N=40$.

Figure 12

Difference between the masses predicted by the Bethe-Weizsäcker formula [Eq. (10)] and the experimental values as a function of $N$ for $Z=28,29$, and 31. Data are from this work, complemented by data from Ref. [40].