Masses of neutron-rich Ni and Cu isotopes and the shell closure at Z = 28 , N = 40

Abstract.The Penning trap mass spectrometer JYFLTRAP, coupled to the Ion Guide Isotope Separator On-Line (IGISOL) facility at Jyväskylä, was employed to measure the atomic masses of neutron-rich 70-73Ni and 73, 75Cu isotopes with a typical accuracy less than 5keV. The mass of 73Ni was measured for the first time. Comparisons with the previous data are discussed. Two-neutron separation energies show a weak subshell closure at 6828Ni40 . A well established proton shell gap is observed at Z = 28 .


Introduction
Recent mass measurements on radioactive nuclei have focused on understanding the evolution of nuclear structure towards more neutron-rich nuclei. These measurements have been partly motivated by nuclear astrophysics as the rapid neutron capture process flows along the neutron-rich nuclides [1]. In addition these nuclei can be used to study nuclear-structure phenomena, such as shell-quenching, subshell closures and the evolution of the shell closures when moving towards very neutron-rich nuclei.
A subshell closure at nucleon number 40 has been studied in semidoubly-magic 90 Zr (Z = 40, N = 50) [2] and 68 Ni (Z = 28, N = 40) nuclei [3,4]. The spin-dependent neutron-proton interaction is responsible for the changes in the single-particle orbital spacings. For example, at N = 40, the subshell closure in 68 Ni originates from a relatively large spacing between the 2p 1/2 and 1g 9/2 neutron orbitals, but this stability effect disappears already at 70 Zn and 66 Fe which have quite low 2 + excitation energies [5].
The N = 40 subshell closure has been observed to be even weaker than the Z = 40 subshell closure. For 68 Ni experimental results show contradictory evidence for the subshell closure [6][7][8][9]. The first excited state in 68 Ni is a e-mail: saidur.rahaman@phys.jyu.fi b Present address: Department of Physics, University of Liverpool, Liverpool L69 3BX, UK. a 0 + state observed at much higher energies than the first excited states in neighbouring even-even nuclei. Also the 2 + 1 state in 68 Ni has a large excitation energy and the B(E2, 0 + gs → 2 + 1 ) is quite small supporting a semidoublymagic character of this nucleus [9]. On the other hand, observed two-neutron separation energies and shell gap energies have not shown the N = 40 subshell closure at Z = 28 [7]. Some suggested explanations are that the twoneutron separation energies are free from pairing effects, whereas pair scattering of neutrons counteracts the magicity at N = 40. In addition, the 2 + excitation can be hindered by a parity change across the N = 40 subshell [9]. As the neutron shell gap energy of 68 Ni is based on the mass of 70 Ni known with a modest accuracy, a mass measurement of 70 Ni is crucial for the possible observation of the subshell closure in the neutron shell gap energies.
Another interest of the mass measurements of the nickel isotopes is triggered by the recent prediction of the tensor force calculation [10] which suggests a possible weakening of the Z = 28 proton shell gap beyond N = 40. Shell structure in the nucleus can change due to the tensor force which is a part of the meson exchange processes predicted by Yukawa [11] in nucleon-nucleon interactions. In the case of exotic nuclei, the single-particle properties can have distinct characteristics due to the tensor force [12] and the neutron-skin effect [13], that are not seen in stable nuclei. The tensor force is included in the Gognytype mean-field model [14] (called GT2) calculations and detailed results of the single-particle energies (SPEs) for 1f 7/2,5/2 and 2p 3/2,1/2 for nickel isotopes are discussed in ref. [10]. The model predicts that as the neutron occupancy increases in the 1g 9/2 orbital the neutron orbit stays rather constant in energy, however, the 1f 7/2 and 1f 5/2 proton orbits move closer to each other thus reducing the Z = 28 proton shell gap energy at 78 Ni. A precise mass value of the neutron-rich nickel isotopes can be used to test this theoretical prediction.
In this work we present precision mass data of the neutron-rich nickel and copper isotopes obtained at JYFLTRAP to probe the issues raised above. The previous direct mass measurements in this region were carried out at the time-of-flight isochronous (TOFI) spectrometer at Los Alamos [15,16] and at the Penning trap mass spectrometer ISOLTRAP at CERN, Geneva [7]. However, the large uncertainty in the mass excess of 70 Ni prevents a precise calculation of the neutron shell gap energy of 68 Ni and the pairing energy of 69 Ni. The masses of neutron-rich 70-73 Ni and 73,75 Cu isotopes are presented in this work. The direct mass measurement of 73 Ni is reported for the first time. These mass values were used to calculate twoneutron separation, neutron shell gap and pairing energies in this region and to study the evolution of the subshell closure in 68 Ni and proton shell gap energies for Z = 28.

Experimental setup and analysis
JYFLTRAP [17] is an ion trap experiment for cooling, bunching, isobaric purification and precision mass measurements of radioactive ions produced at the IGISOL facility [18]. A schematic drawing of the JYFLTRAP setup is shown in fig. 1. The radioactive nuclides were produced in a proton-induced fission reaction by bombarding a natural uranium target of thickness 15 gm/cm 2 with a 30 MeV proton beam from the Jyväskylä K-130 cyclotron. Radioactive ions are extracted from the gas cell by helium gas flow and guided by the sextupole ion guide (SPIG) into a differential pumping stage where they are accelerated to 30 keV and mass-separated with a 55 • dipole magnet. A mass-resolving power (M/∆M ) of up to 500 can be achieved. The production rates of the studied nuclei varied from 20 ions/s to a few ions/s for the most exotic isotopes measured at a position before they enter to the radiofrequency quadrupole (RFQ) cooler and buncher. In this device the ions are cooled by collisions with helium buffer gas and are accumulated at the end of the RFQ structure. The ions are extracted at low energy as a short bunch with a time structure of about 15 µs [19] and are injected into the purification Penning trap, where the mass selective buffer gas cooling technique is applied for further cooling and isobaric cleaning [20,21]. The mass-resolving power of the purification trap is on the order of 10 5 . The purified and cooled ions are finally transported to the precision Penning trap where the cyclotron frequency (ν c ) is measured by employing the time-of-flight technique [22]. A typical time-of-flight resonance of 73 Ni + radioactive ions is shown in fig. 2. An excitation time T ex = 400 ms was used in the case of 73 Ni and 73,75 Cu isotopes, whereas T ex = 800 ms was used for 70-72 Ni isotopes. The cyclotron frequency is given by where B is the magnetic field, m is the mass and q the charge state of the ion. To calibrate the magnetic field the cyclotron frequency (ν c,ref ) of a precisely known reference mass (m ref ) is measured. The atomic mass of the ion of interest is then determined using the equation where r = ν c,ref /ν c is the frequency ratio and m e is the electron mass. A typical accuracy below 5 keV has been obtained in this experiment. A detailed mass measurement procedure at JYFLTRAP can be found in refs. [23,24]. Three known systematic uncertainties were taken into account in the cyclotron frequency determinations. These are the uncertainties due to the temporal magnetic-field fluctuation, the mass difference between the reference ion to the ion of interest m−m ref and the frequency shift due to contaminating ions in the trap.
The linear drift of the magnetic field was taken into account by the interpolation of the reference cyclotron frequencies. In order to quantify the short temporal magnetic field fluctuations continuous cyclotron frequency Table 1. Results from the analysis of 73,75 Cu and 70-73 Ni measured at JYFLTRAP. The measured average frequency ratio r and its uncertainty is presented. T 1/2 represents the beta decay half-life of the studied nuclei. M Eex represents the experimental mass excess obtained from the cyclotron frequency ratio. M E lit are the AME03 values [25]. The last column gives the difference between the AME03 and JYFLTRAP values ∆ = M Eex − M E lit .   fig. 3. The uncertainty due to magnetic-field fluctuation was estimated from the linear fit to be 3.22(16) × 10 −11 /min. The offset of the linear fit was 9.2 × 10 −9 and it represents the statistical uncertainty of an individual frequency measurement for 57 Fe + files. The count rate class and the mass-dependent systematic uncertainties were taken into account in the same way as explained in ref. [24] and references therein.

Results
The results of the mass measurements for 73,75 Cu and 70-73 Ni are summarized in table 1 and discussed in the following section. The frequency ratio of each isotope is given with respect to the cyclotron frequency of the stable 72 Ge + isotope. The mass of the 72 Ge isotope is known with an uncertainty of 1.6 keV [25]. In table 1 the column M E ex presents the JYFLTRAP mass excess value with the final uncertainty in parenthesis. The uncertainty contains the statistical and systematic uncertainties. Figure 4 represents the differences between the mass excess measured at JYFLTRAP and the TOFI and Atomic Mass Evaluation 2003 (AME03) values [25]. The JYFLTRAP measurements reduced the uncertainties by a factor of about 100 for each nuclei. 73 Ni was measured for the first time 1 .  The two-neutron separation energy S 2n can be obtained by using the following formula: where M (A, Z) is the mass of an isotope and M (1, 0) is the neutron mass. S 2n is shown as a function of neutron number in fig. 5 for Z = 26-31. The filled circles are from this work and the data are completed by the values from the AME03 [25]. Generally, S 2n decreases smoothly with neutron number and shell effects appear as a discontinuity. Small discontinuities are observed in the cases of 67,68 Ni (more bound), 70,71 Cu (less bound) and 72 Ga (less bound). Moreover, in the case of 68 Ni this deviation is less than 1 MeV which is rather small compared to a regular shell closure.
In fig. 5 a clear change of the slope beyond N = 40 is observed. This may be due to the effect of the tensor force. Filling more neutrons in the 1g 9/2 orbit results in the pulling-down of the orbit. In addition as more neutrons occupy the 1g 9/2 orbit the 1f 5/2 and 2p 3/2 orbits are crossing each other after N = 40. The results of these two effect may increase the S 2n energies, hence the slope will be reduced beyond N = 40. Figure 6 displays S 2n as a function of proton number for even neutron numbers. The neutron shell gap energy is define as ∆(N ) = S 2n (Z, N ) − S 2n (Z, N + 2), where N defines the neutron number. The vertical distance between two consecutive isotones in fig. 6 represents the neutron shell gap energies. A small enhancement of the neutron shell gap energy at N = 40 for Z = 28 is observed but far below that expected from a shell closure. This can be explained by considering N = 40 as a weak subshell closure.

Proton shell gap energies for Z = 28
The two-proton separation energy S 2p is extracted by using the following formula: where M (1, 1) is the hydrogen mass. S 2p is plotted as a function of the neutron number in fig. 7 for even Z = 26-32. In this plot the gap between the Z = 28 to Z = 30 chains yield the proton shell gap energy for Z = 28. The experimental data points end at N = 41 for the Z = 28 isotope chain. According to the tensor force calculations, as more neutrons are occupying 1g 9/2 orbit 1f 7/2 and 1f 5/2 orbits are coming closer to each other resulting a reduction of the proton shell gap energy at Z = 28 while going from N = 40 to N = 50. In fig. 7 at N = 41 for Z = 28 a tendency of decreasing of the proton shell gap energy is noticed which is in agreement with the tensor force prediction. However, the next point at N = 42 has a higher shell gap energy but with a large uncertainty. This uncertainty comes from the mass of 68 Fe. Therefore more experimental mass data are required, in particular the masses of all n-rich Fe isotopes with reduced uncertainties to ascertain the observed trend.

Conclusions
In conclusion the masses of the neutron-rich nickel and copper isotopes were measured at JYFLTRAP. The mass of 73 Ni was measured for the first time. The shell structure around the N = 40 region was investigated. Precise mass values in this region are able to clarify the contradictory nature of the shell structure in 68 Ni. A local weak discontinuity is observed in the two-neutron separation energy for 68 Ni. A clear change of the slope in the two-neutron separation energy plot is observed beyond N = 40. A small enhancement of the neutron shell gap energy is noticed at Z = 28 for N = 40 compared to N = 38 and 42 which is consistent with the recent studies by other experiments [6,9]. From these observations one can conclude that 68 Ni is a weak subshell closure. A detailed review of the theoretical study of shell closure and an indication of weak subshell closure is discussed in ref. [26]. A trend of the possible reduction of the proton shell gap energy is observed which is in agreement with the tensor force prediction. More experimental masses are required to be able to extract the proton shell gap energies around Z = 28. In the future JYFLTRAP aims to measure the masses of the neutronrich nickel and iron isotopes to continue with this open question.