Spectroscopic overlaps between states in 16 C and 15 C IV (with WBT and NuShell)

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1 Spectroscopic overlaps between states in 16 C and 15 C IV (with WBT and NuShell) Y. Satou January 26, 2014 Abstract Shell-model calculations were performed to extract spectroscopic overlaps between states in 16 C and two bound states (the 1/2 + ground state and the 5/2 + first excited state at 0.74 MeV) and an unbound state (the first 3/2 + shell-model state) in 15 C. The WBT shell-model interaction was used in the calculation employing the NuShell shell-model code. The results are presented. 1 Introduction To investigate decay properties of states in 16 C, shell-model calculations were performed. Spectroscopic factors C 2 S giving overlaps of them with two bound states in 15 C, the 1/2 + ground state and the 5/2 + first excited state at 0.74 MeV, were derived. Those with an unbound state in 15 C, the first 3/2 + shell-model state, were also derived. The calculations were done using the code NuShell [1] with the WBT interaction [2] in the spsdpf model space and the 0 hω configuration (only the 1p configuration in 15 C was taken into account). 2 Results Tables similar to the Table 1 of Ref. [3] were made. The results for positive parity states are given in Tables 1-2, while those for negative parity states in Tables 3-6. The one-neutron knockout cross sections in the tables are from Ref. [4]. Sound spin-parity assignments are available for all file bound excited states (all are positive parity). For unbound states unambiguous spin-parity assignments have been done for the first 2 state at 5.45 MeV [5] and the 5 state at 8.92 MeV [6]. For some of the excited states in 16 C relative branching ratios for decay leading to the first excited 5/2 + state at 0.74 MeV in 15 C, Γ 5/2 +/(Γ g.s. + Γ 5/2 +), have been calculated. The results are listed in the Tables. It was assumed in the calculation that the partial width is proportional to the spectroscopic factor C 2 S, the factor kr, and the transmission through the centrifugal barrier v l : Γ C 2 S kr v l, (1) where R was taken to be the radius of the (daughter) nucleus. The factor k is the wave ysatou/r364n/16c c2s wbt nushell.pdf 1

2 Ex Edecay2 3/2 + Edecay1 Sn=4.25 MeV 0.74 MeV 1/ C 5/ C Figure 1: Decay diagram of states in 16 C into the ground and first excited (0.74 MeV) states in 15 C. Spectroscopic overlap with the first shell-model 3/2 + state (particle unbound) was additionally taken into account. number of the relative motion of the decay given by: k = 2µEdecay hc, (2) where E decay is the decay energy and µ is the reduced mass of the decay products. The factor kr in Eq.(1) is proportional to the outgoing flux; it takes care of the phase-space factor of the two-body decay [7]. The factor v l dealing in the transmission of the neutron through the centrifugal barrier (in a square potential) is given for each l value as follows [8, 9]: with v 0 = 1, (3) v 1 = v 2 = v 3 = x x2, (4) x x 2 + x4, (5) x x 2 + 6x 4 + x6, (6) x = kr. (7) 2

3 Possible interference effects among transitions having the same initial and final states were not taken into account. It is to be noted that the states in 16 C located above the two-neutron threshold of MeV (4.25 MeV MeV) can decay by emitting two neutrons, and that the states above 7.35 MeV (4.25 MeV MeV) can decay to the second excited 1/2 state at 3.10 MeV in 15 C. In the present calculation, these branches were not taken into account. References [1] Nushell@MSU, B.A. Brown and W.D.M. Rae, MSU-NSCL report (2007). [2] E.K. Warburton and B.A. Brown, Phys. Rev. C 46 (1992) 923. [3] A. Spyrou, et al., Phys. Lett. B 683 (2010) 129. [4] ysatou/r364n/sigma 1n.pdf [5] Y. Satou, et al., Phys. Lett. B 728 (2014) 462. [6] H.G. Bohlen, et al., Phys. Rev. C 68 (2003) [7] Jean-Louis, et al., Fundamentals in Nuclear Physics, Springer, [8] A. Bohr and B.R. Mottelson, Nuclear Structure I, World Scientific, [9] J.M. Blatt and V.F. Weisskopf, Theoretical Nuclear Physics, Dover,

4 Table 1: Shell-model calculations for the spectroscopic overlap between positive parity states in 16 C and the ground (1/2 + ; 0.0 MeV) and first excited (5/2 + ; 0.74 MeV) states in 15 C. The results for the overlap with the first shell-model 3/2 + state (particle unbound) are also listed. The calculation was done using NuShell [1] with the WBT [2] interaction. The quantity σ 1n in the second column refers to the one-neutron knockout cross section producing excited states in 16 C via knockout from 17 C on a proton target and at an incident energy of 70 MeV/nucleon (taken from Ref. [4]) g.s. (1/2 + ) (1s 1/2 ) 0.74 (5/2 + ) (0d 5/2 ) (3/2 + ) (0d 3/2 ) g.s. (1/2 + ) (0d 5/2 ) (0d 3/2 ) 0.74 (5/2 + ) (0d 5/2 ) (0d 3/2 ) (1s 1/2 ) (3/2 + ) (0d 5/2 ) (0d 3/2 ) (1s 1/2 ) g.s. (1/2 + ) (1s 1/2 ) 0.74 (5/2 + ) (0d 5/2 ) (3/2 + ) (0d 3/2 ) g.s. (1/2 + ) (0d 5/2 ) (0d 3/2 ) 0.74 (5/2 + ) (0d 5/2 ) (0d 3/2 ) (1s 1/2 ) (3/2 + ) (0d 5/2 ) (0d 3/2 ) (1s 1/2 ) (5/2 + ) (0d 5/2 ) (0d 3/2 ) (3/2 + ) (0d 5/2 ) g.s. (1/2 + ) (0d 5/2 ) 0.74 (5/2 + ) (0d 5/2 ) (0d 3/2 ) (1s 1/2 ) (3/2 + ) (0d 5/2 ) (0d 3/2 ) 4

5 Table 2: Continuation of Table g.s. (1/2 + ) (0d 5/2 ) (0d 3/2 ) 0.74 (5/2 + ) (0d 5/2 ) (0d 3/2 ) (1s 1/2 ) (3/2 + ) (0d 5/2 ) (0d 3/2 ) (1s 1/2 ) (5/2 + ) (0d 5/2 ) (0d 3/2 ) (3/2 + ) (0d 5/2 ) g.s. (1/2 + ) (0d 5/2 ) 0.74 (5/2 + ) (0d 5/2 ) (0d 3/2 ) (1s 1/2 ) (3/2 + ) (0d 5/2 ) (0d 3/2 ) g.s. (1/2 + ) (0d 3/2 ) (1s 1/2 ) 0.74 (5/2 + ) (0d 5/2 ) (0d 3/2 ) (3/2 + ) (0d 5/2 ) (0d 3/2 ) (1s 1/2 ) 5

6 Table 3: Same as Table 1 except that the spectroscopic overlap is between negative parity states in 16 C and the two bound states and an unbound state in 15 C g.s. (1/2 + ) (0f 5/2 ) (1p 3/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) g.s. (1/2 + ) (0f 7/2 ) (0f 5/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) g.s. (1/2 + ) (1p 3/2 ) (1p 1/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (3/2 + ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) g.s. (1/2 + ) (1p 1/2 ) (5/2 + ) (0f 5/2 ) (3/2 + ) (1p 3/2 ) g.s. (1/2 + ) (1p 3/2 ) (1p 1/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (3/2 + ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) 6

7 Table 4: Continuation of Table g.s. (1/2 + ) (0f 5/2 ) (1p 3/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) g.s. (1/2 + ) (1p 3/2 ) (1p 1/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (3/2 + ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) g.s. (1/2 + ) (0f 5/2 ) (1p 3/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) g.s. (1/2 + ) (0f 7/2 ) (0f 5/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) 7

8 Table 5: Continuation of Table g.s. (1/2 + ) (0f 5/2 ) (1p 3/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) g.s. (1/2 + ) (0f 7/2 ) (0f 5/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) g.s. (1/2 + ) (1p 3/2 ) (1p 1/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (3/2 + ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) g.s. (1/2 + ) (1p 1/2 ) 0.74 (5/2 + ) (0f 5/2 ) (3/2 + ) (1p 3/2 ) g.s. (1/2 + ) (0f 7/2 ) (0f 5/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) 8

9 Table 6: Continuation of Table g.s. (1/2 + ) (0f 5/2 ) (1p 3/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) g.s. (1/2 + ) (1p 3/2 ) (1p 1/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (3/2 + ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) g.s. (1/2 + ) (0f 7/2 ) (0f 5/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) g.s. (1/2 + ) (0f 7/2 ) (0f 5/2 ) 0.74 (5/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) (1p 1/2 ) (3/2 + ) (0f 7/2 ) (0f 5/2 ) (1p 3/2 ) 9

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