University of Pennsylvania ScholarlyCommons Department of Physics Papers Department of Physics 7-30-2007 Two-Proton Decay Energy and Width of 19Mg(g.s.) H. Terry Fortune University of Pennsylvania, [email protected] Rubby Sherr Princeton University Follow this and additional works at: https://repository.upenn.edu/physics_papers Part of the Physics Commons Recommended Citation Fortune, H. T., & Sherr, R. (2007). Two-Proton Decay Energy and Width of 19Mg(g.s.). Retrieved from https://repository.upenn.edu/physics_papers/171 Suggested Citation: H.T. Fortune and R. Sherr. (2007). Two-proton decay energy and width of 19Mg(g.s.). Physical Review C 76, 014313. © 2007 The American Physical Society http://dx.doi.org/10.1103/PhysRevC.76.014313 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/physics_papers/171 For more information, please contact [email protected]. Two-Proton Decay Energy and Width of 19Mg(g.s.) Abstract We use a weak-coupling procedure and results of a shell-model calculation to compute the two-proton separation energy of 19Mg. Our result is at the upper end of the previous range, but 19Mg is still bound for single proton decay to 18Na. We also calculate the 2p decay width. Disciplines Physical Sciences and Mathematics | Physics Comments Suggested Citation: H.T. Fortune and R. Sherr. (2007). Two-proton decay energy and width of 19Mg(g.s.). Physical Review C 76, 014313. © 2007 The American Physical Society http://dx.doi.org/10.1103/PhysRevC.76.014313 This journal article is available at ScholarlyCommons: https://repository.upenn.edu/physics_papers/171 PHYSICAL REVIEW C 76, 014313 (2007) Two-proton decay energy and width of 19Mg(g.s.) H. T. Fortune Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA R. Sherr Department of Physics, Princeton University, Princeton, New Jersey 08544, USA (Received 27 July 2006; published 30 July 2007) We use a weak-coupling procedure and results of a shell-model calculation to compute the two-proton separation energy of 19Mg. Our result is at the upper end of the previous range, but 19Mg is still bound for single proton decay to 18Na. We also calculate the 2p decay width. DOI: 10.1103/PhysRevC.76.014313 PACS number(s): 21.10.Dr, 21.10.Sf, 23.50.+z, 27.20.+n I. INTRODUCTION described as (sd)2(1p)−1. However, weak coupling would 2 18 18 Along the proton drip line, many of those proton-rich nuclei identify the (sd) part with the g.s. of O and Ne. And those states contain significant (∼10%) core excitation. To the extent have not had their masses determined. In almost all cases, 4 −2 the neutron-rich mirrors of these nuclei have well-determined that this (sd) (1p) component contains two holes in the masses. In the absence of experimental evidence on the proton- p1/2 orbital, weakly coupling a p1/2 hole to that component rich masses, a procedure that accurately calculates Coulomb would violate the Pauli principle. This is a clear example of a energy differences is useful in estimating them. Of special situation in which the particles in the parent state are different 19 from those in the particle-hole state. A major manifestation interest is Mg, which may be the best candidate among light 18 + 6 of this effect is that even though O has three low-lying 0 nuclei (after Be, of course) to be a simultaneous 2p emitter. 2 2 For nuclei near A = 20, the Coulomb energy difference states [primarily linear combinations of (1d 5/2) ,(2s1/2) , for ground states (g.s.) of mirror nuclei (which have identical and 4p-2h], coupling a p1/2 hole to them results in only two low-lying 1/2− states in 17N[4,5]. nuclear energies) is quite sensitive to the relative population 17 of nucleons in the 2s1/2 and 1d5/2 orbitals. The larger the If we were to calculate the mass excess of N in pure 17 = 18 + 15 − 16 + 2s1/2 occupancy, the lower will the state be in the proton-rich weak coupling, we would get N O N O 2(a + b/4) = 7.675 MeV, to be compared with the known member of the mirror pair. This effect has long been called 17 the Thomas-Ehrman shift (TES), but it is nothing special. It mass excess [6] of 7.871 MeV for N.(Wetakethevalue + 16 comes naturally out of a single-particle type calculation in a of a b/4 from N.) This 200 keV discrepancy is easily understandable from the injustice this calculation does to the diffuse potential well. 17 If core excitation can be neglected, these Coulomb energies Pauli principle. In reality, N is better described as a p1/2 hole in the lowest (sd)20+ state, not the physical 18O(g.s.). can usually be reliably computed using shell-model wave A similar calculation for 17Ne misses the mass excess by functions and coupling s or d nucleons to appropriate core a different amount. The fact that this simple (and incorrect) states (frequently many in number). If the nucleus consists calculation misses 17N and 17Ne by different amounts means of valence nucleons coupled to a core containing vacancies that such a calculation would also miss the 17N-17Ne Coulomb in a lower shell, the shell-model calculation is usually not so energy (see below). straightforward. In some of these cases, e.g., a few sd-shell For 17N and 17Ne we have demonstrated [7] that coupling nucleons coupled to one or two p-shell holes, weak-coupling s2 and d2 nucleons to the physical g.s. of 15N and 15O can procedures (suitably applied) are reasonably reliable. In certain easily provide the known g.s. Coulomb energy, with an s2 instances, a combination of shell model plus weak coupling is component of 22% (24 ± 3% in Ref. [8]), very close (but appropriate. For example, such a hybrid calculation gave rea- larger than) the known s2 occupancy [2]in18O [19% of sonable agreement [1] for many levels of the 18O-18Ne pair. In the total wave function, but 21% of the (sd)2 component]. that example, the states of 18Owere[2] linear combinations of Other estimates [9] provide 40–50% s2 in 17Ne, and some [10] two-particle (sd)2 configurations and a collective component even suggest a preponderance of s2 over d2. Two different that was primarily (sd)4(1p)−2. The assumption that the (sd)4 shell-model approaches [8] gave satisfactory agreement for states behaved as the low-lying positive-parity states of 20Ne Coulomb energies of several excited states of 17Ne. These worked well. As the (sd)4 part of the 4p-2h structure was the states were then used as cores to compute the g.s. mass of same for 18O and 18Ne, the Coulomb energy for the 4p-2h 18Na, with reasonable success. [8]Weturnnowtothecaseof component involved only the 14O-14C mass difference and the 19Mg. weak-coupling Coulomb parameter c. The nucleus 19Mg is expected to be unbound with respect In certain other cases, weak-coupling alone (in the Banzal- to 2p decay to 17Ne, but bound for p decay to 18Na. It may French-Zamick sense [3]) might be thought to be appropriate, be the best candidate for simultaneous 2p decay after 6Be. but further inspection reveals that not to be so. One such Grigorenko et al. [9] performed calculations for 17Ne and 17 17 19 19 example is the pair N- Ne. Both are thought to be well Mg. They estimate for Mg a value E2p = 550–850 keV 0556-2813/2007/76(1)/014313(7) 014313-1 ©2007 The American Physical Society H. T. FORTUNE AND R. SHERR PHYSICAL REVIEW C 76, 014313 (2007) (unbound). However, they may have too much s2 admixture TABLE I. Weak-coupling estimates of mass excess (MeV) for in their wave function. They estimate 40–50% s2 in 17Ne, mirrors of 17,18,19N. whereas we prefer (as stated above) significantly less—about 22–24%. Because of the TES, having too much s2 will cause Nucleus Weak coupling Measured Difference the proton-rich nucleus to be less unbound. In Ref. [9], the 17Ne 16.725(15) 16.461(27) [6]0.264(31) proton-rich member of a mirror pair has higher s1/2 occupancy 18Na 25.461(23) 25.06(13) [17]or 0.401(132) than the neutron-rich member. In all our calculations, these are 25.04(17) [18] 20 equal in the mirror pair. For Mg we found [11] that the 11th 19Mg 32.389(32) ? and 12th proton were predominantly in the d orbital, so that the s2 occupancy in 20Mg should be approximately equal to that in 18Ne. Before we attempt to calculate the 19N-19Mg standable. Slightly different s2/d2 ratios in 18Ne and 17Ne also Coulomb energy with the shell model, we estimate it using contribute to the difference. For 18N-18Na, the parent nuclei are weak coupling considerations. 19O and 19Na (see Fig. 1), and the first two states of those two nuclei seem to have very little 2s1/2 occupancy. Of course, in this case, weak coupling provides an estimate of the energy + II. WEAK COUPLING of the doublets arising from coupling a p1/2 hole to the 5/2 and 3/2+ states in 19O and 19Na. The g.s. of 18Na is 1−, and Usually, Coulomb energy differences of mirror nuclei will hence must involve the 3/2+ state of 19Na, not the 5/2+, which depend on the Coulomb parameter c when computed in weak- is the g.s.