Odd-even staggering in yields of neutron-deficient nuclei produced by projectile fragmentation

Background: Fragment yields exhibit a strong odd-even staggering (OES). This OES has been experimentally observed in different fragmentation reactions with different projectile-target combinations. However, the experimental data are still scarce for fragments close to drip lines and the origin of this OES is not well understood.

Purpose: More experimental data are needed to explore the origin of this OES in fragment yields and to validate fragmentation reaction models, especially for nuclei close to the drip lines. To study the pronounced OES near the proton drip line, we measured the yields of $T_z=-1$ and $T_z=-3/2$ nuclei over a wide range of mass number.

Methods: The combination of a fragment separator and a storage ring at the Heavy Ion Research Facility in Lanzhou has been used to measure the yields of $T_z=-1$ and $T_z=-3/2$ fragments, produced by ${}^{58}\mathrm{Ni}$ projectiles impinging on a beryllium target at an energy of about 463 MeV/nucleon.

Results: A very strong OES is observed in the measured yields of both $T_z=-1$ and $T_z=-3/2$ fragments. Our experimental data demonstrate that the shell structure has a significant impact on the magnitude of this OES. A comparison of different fragmentation reaction data indicates that this OES is almost independent of the projectile-target combinations and the fragmentation energy between 140 and 650 MeV/nucleon.

Conclusions: Our study reveals that the OES of fragment yields originates mainly from the OES of particle-emission threshold energies, which is very close to the OES of fragment yields when the Coulomb barrier is considered in particle-emission threshold energies.

Figure 1

The measured revolution-time spectrum in the time window of $T_z=-3/2$ nuclides of interest, which were produced in ${}^{58}\mathrm{Ni}$ fragmentation reactions on a Be target at an energy of about 463 MeV/nucleon. The inset shows the well-resolved peaks from ${}^{45}\mathrm{Cr}^{24+}$ and ${}^{30}\mathrm{S}^{16+}$. This spectrum was measured with the RIBLL2-CSRe facility being optimized for the transmission of $T_z=-3/2$ nuclides centered around ${}^{47}\mathrm{Mn}$. Measured $T_z=-3/2$ nuclei together with their mass numbers are indicated by red letters. The upper parts of the peaks from ${}^{15}\mathrm{O}$ and ${}^{17}\mathrm{F}$ have been cut to clearly show other peaks of interest.

Figure 2

(a) Yields of $T_z=-3/2$ and $T_z=-1$ nuclei measured in this ${}^{58}\mathrm{Ni}$ fragmentation reaction experiment. The error is determined by the systematic uncertainty of the estimations of transmission efficiencies (10%) and the statistical uncertainty. Note that the yields are plotted on a logarithmic scale. (b) Magnitudes of the OES-FY for $T_z=-3/2$ and $T_z=-1$ nuclei measured in this experiment as well as those in other experimental data from the fragmentation of ${}^{58}\mathrm{Ni}, {}^{48}\mathrm{Ca}$, and ${}^{40}\mathrm{Ca}$ projectiles reported in Refs. [1, 3]. They are calculated according to Eq. (1). These experimental data are also compared with predictions of the abrasion-ablation model [29], where the evaporation parameters are similar to those used in Refs. [6, 49, 51].

Figure 3

(a) The particle-emission threshold energy (PETE) for $T_z=-3/2$ and $T_z=-1$ nuclei. The PETE value ($S_p$) from AME'03 [56] is compared with that from AME'12 [55] as well as with the sum of $S_p$ from AME'12 and the Coulomb barrier. For ${}^{43}\mathrm{V}, {}^{47}\mathrm{Mn}$, and ${}^{51}\mathrm{Co}$, negative error bars of the PETE from AME'03 are out of range and are not shown. For $T_z=-3/2$ nuclei, the PETE from AME'03 is not measured by experiments, except for ${}^{45}\mathrm{Cr}$. In AME'12, the PETE is from experimental data, except for ${}^{52}\mathrm{Co}$ and ${}^{53}\mathrm{Ni}$. In the case where the Coulomb barrier is considered, the error of PETE is not given since the Coulomb barrier is calculated from a theoretical model. (b) Magnitudes of the OES in PETE for $T_z=-3/2$ and $T_z=-1$ nuclei. They are calculated with Eq. (1), where yields are replaced by PETE values. For $T_z=-3/2$ nuclei, positive error bars of magnitudes calculated from AME'03 are out of range.