A theoretical perspective on triggered gamma emission from 178 Hf m2 isomer

1. A theoretical perspective on triggered gamma emission from 178Hfm2 isomer Shuifa Shen School of Nuclear Engineering and Technology, East China Institute of Technology, Fuzhou 344000, Jiangxi, People’s Republic of China

2. Introduction Long-lived high-energy nuclear isomeric states are suitable media for storing the energy. The controlled release of energy stored in nuclear isomeric samples will produce powerful pulsed-sources of gamma ray radiation. That is why, at present, this field is at the focus of a great scientific and technological interest. In addition, the possibility that the gamma bursts produced to have coherence and directionality (gamma-ray lasers) brings even more attention. It would be the very best of all possibilities to be able to immediately realize the release of high energy densities into a coherent radiation field.

3. However, simply the induced emission of gamma rays from an isomeric sample would be of considerable technological significance. That goal is close at hand. Once attained, the development of increasing levels of coherence can be approached as a next logical objective [1]. The triggering of the gamma radiation has been the object of our research as a first step in the pumping of a gamma-ray laser. In previous years, many efforts and concepts have been put forward to find the best isomeric candidates and solutions to control the release of their energy. The top position of the most interesting candidates list is occupied by 178Hfm2 isomer [2, 3] because it is long lived, available in research quantities, has a well known decay scheme, high excitation energy, a stable ground state, and targets of the isomeric Hf can be fabricated.

4. But up to now the induced  emission in the case of spin-16, 2.446 MeV isomer in 178Hf is not established. The works carried out by Collins and coworkers [3-5] presented positive results, but they were not reproduced by much more elaborated experiments [6-9]. However, it is interesting to study the process in the case of 16+ isomer of 178Hf from the nuclear physics point of view. By the way, although the experimental results and theoretical estimates in the work of Carroll et al. [9] did not support the low energy depletion of 178Hfm2 isomer, they did not deny the existence of lower-lying intermediate states (relative to the isomer). • [3] C. B. Collins et al., Phys. Rev. Lett. 82 (1999) 695. • [4] C. B. Collins et al., Phys. Rev. C 61 (2000) 054305. • [5] C. B. Collins et al., Europhys. Lett. 57 (2002) 667. • [6] I. Ahmad et al., Phys. Rev. Lett. 87 (2001) 072503. • [7] I. Ahmad et al., Phys. Rev. C 67 (2003) 041305. • [8] I. Ahmad et al., Phys. Rev. C 71 (2005) 024311. • [9] J. J. Carroll et al., Phys. Lett. B 679 (2009) 203.

5. Fig. 1. Schematic diagram illustrating the process of triggered gamma-ray emission from a nuclear isomer.

6. This is the two-step process of triggered gamma-ray emission. A nucleus in an isomeric state is first excited to an intermediate state by absorption of an incident photon. An intermediate state may serve as a “gateway” that connects the isomer to the ground state (g.s.). Realistically speaking, even ignoring a possible role of the K quantum number, this requires the multipolarities of the transition from the isomer to intermediate state and the transition from the intermediate state to the ground state to be small. Obviously, this conflicts with the fact that a large angular momentum difference exists between isomer and ground state. This contradiction may disappear if the final state is not the ground state and the full spontaneous decay cascade from the final state can rid the nucleus of its excess angular momentum.

7. Level schemes like that reported in Ref. [5] provide important guidance to known electromagnetic transitions that might enable triggering. It was determined that the 14−, 68 s isomer (with K=14) decayed with several branches, one of which led to the 4s isomer band and another of which led to the 31year, 16+ isomer (K=16). The essential point is that the latter transition has an M2 character and with L=2 and K=2, there is no K hindrance. Thus, the 126 keV transition from the 16+ isomer to the 14−isomer should produce triggered gamma emission. • [5]T.L. Khoo and G. Løvhøiden, Phys. Lett. B 67, 271 (1977).

8. In determining the favorable conditions for triggering gamma-ray emission from the isomer, it is necessary to have information on the structure of possible gateway states, as well as possible paths of electromagnetic transitions to and from these states. Experimentally, only a few states close to the 178Hf isomer have been observed and documented in the literature [6, 7]. The purpose of the present work is to demonstrate that the potential-energy surfaces (PES) calculations [8] is an appropriate theory for studying high-spin isomers and associated excitations, including potential gateway states; and to show that in the 178Hf case, in order to trigger emission from the 16+ isomer with low-energy photons, there are a few gateway states that may be supplied from our theoretical consideration. • [6]S.M. Mullins, et al., Phys. Lett. B 393 (1997) 279; • S.M. Mullins, et al., Phys. Lett. B 400 (1997) 401. • [7]A.B. Hayes, et al., Phys. Rev. Lett. 89 (2002) 242501.

9. 2. Calculations and discussion • The present work employs the nonaxial deformed Woods-Saxon (WS) potential [9] with universal parameters [10]. The monopole pairing strength (G) is obtained by the average gap method [11]. To avoid the spurious phase transition encountered in the BCS approach, we have performed approximate particle number projection by means of the Lipkin-Nogami (LN) method [12, 13]. The total energy of a configuration can be decomposed into a macroscopic part, that is obtained from the liquid-drop model with the original parameters of Ref. [14] and a microscopic part resulting from the Strutinsky shell-correction [12, 15], . The constrained configuration energy in the LN approach, which contains the extra Lagrange multiplier, 2, is given by

10. with where S is the proton or neutron seniority for a given configuration (i.e. the number of blocked orbitals with index kj), and N is the proton or neutron number. The blocking effect is achieved by removing the singly occupied orbitals from the LN calculation. The PES’s are calculated in the lattice of quadrupole (2, ) deformations with hexadecapole 4 variation. In the description of qp excitations, axial symmetry at =0 is equivalent to =-120. It is well known that collective rotational bands, conventionally represented at 0, can be built on excited qp configurations. Hence, PES calculations are represented around 0.

11. A realistic treatment of a multiquasiparticle state can be achieved with a configuration-constrained (adiabatic-blocking) calculation of the potential-energy surface [8], i.e., when changing deformation, to always follow and block the given orbitals which are occupied by the specified quasiparticles. The calculated angular-momentum values, energies, and shape parameters for various Nilsson configurations are given in Table I, where N and P denote neutron and proton, respectively, and L1, L2, L3, U1, U2, U3 and U4 for neutron (L1, L2, U1 and U2 for proton) denote their single particle orbitals. They have been indicated in the bottom of Table I. • [8] F.R. Xu, P.M. Walker, J.A. Sheikh, R. Wyss: Phys. Lett. B 435 (1998) 257

12. It appears that the calculated levels at 2.677 and 2.837 MeV lies between 2.405 MeV (corresponds to 31year, K=16+ isomer at 2.446 MeV) and 3.096 MeV (corresponds to K=14- isomer at 2.574 MeV), so these two levels besides K=14- isomeric state are the most likely candidates for photodeexcitation of the spin-16, 31-year isomer. But many important parameters are as yet unknown, and they can be evaluated only after the new experiments carried out.

13. In the present work the calculated PES’s for the g.s., observed K=16+ isomeric state and all other multiquasiparticle states given in Table I suggest a rigidity to axially asymmetric shapes (see, for example, Fig. 2), which is consistent with the result deduced by Andrejtscheff and Petkov using the sum-rule method applying approximations [17]. The rigidity of the ground state is evidenced by the existence of the relatively high-lying  band, whose band head lies at 1175keV [18]. Furthermore in general the multiquasiparticle states are more rigid than the ground state. • [17]W. Andrejtscheff, P. Petkov, Phys. Lett. B329, 1(1994). • [18]A.B. Hayes, D. Cline, C.Y. Wu, M.W. Simon, R. Teng, J. Gerl, Ch. Schlegel, H.J. Wollersheim, A.O. Macchiavelli, K. Vetter, P. Napiorkowski, J. Srebrny: Phys. Rev. Lett. 89 (2002) 242501.

14. Fig. 2. Calculated PES’s for the g.s. (in left) and K=16+ isomer (2-q2-q in right) for 178Hf.

15. Experimentally, the main issue is how to tell if triggered gamma emission has occurred at all. In general, there are a limited number of different methods that can be utilized for the detection of triggered events and determination of the final-state yield [19]: • 1. Detection out-of-beam of short-lived products following triggering of a ‘stable’ (extremely long-lived) isomerso-called activation method; • 2. Detection in-beam of an intensity enhancement of spontaneous decay radiation driven by the external irradiation; • 3. Detection in-beam of a new  line corresponding to the triggering process that doesn’t appear in the spontaneous decay of the isomer; • 4. Detection in-beam of a unique gamma-ray cascade due to triggering that is significantly different from the spontaneous-decay cascade; • 5. Detection out-of-beam of a loss in isomer activity as a result of ‘burn-up’ of part of the metastable population during an intense irradiation; and • 6. Detection in or out-of-beam of an intensity enhancement in the equilibrium daughter radiation after ‘burning’ an isomer to a radioactive state.

16. It should be pointed out here that the low energy  ray say E20keV would have not been visible in the Compton-suppressed Ge detector because it was below the energy threshold and the probability for internal conversion is expected to be greater than for  decay.

17. Triggered emission of gamma rays, releasing the energy stored in long-lived nuclear metastable states, has been experimentally established since 1987 for the depletion of the 1015-year isomer of 180Ta. In the near future, we hope that the triggered gamma emission may be conclusively demonstrated for 178Hf studied in the present work and for other long-lived isomers, such as those of 177Lu and 242Am. Whether they can occur, only experiments will tell.

18. 3. Summary • In summary, we have performed deformation-pairing self-consistent calculations for multi-qp states, with the following results: (i) All multi-quasiparticle states calculated in the present work are approximately axially symmetric with almost the same quadrupole deformation 2 and are rigid to axially asymmetric shapes. (ii) Two levels besides the already known level at 2.574 MeV are found for candidates of the potential gateway states. However, transition-rate calculations are beyond the scope of the present work. Thus, improved experimental methods by which to better examine these claims will be valuable.

19. 本人2010年发表的部分文章： • [1]Shuifa Shen, Guangbing Han, Feng Pan, Jianyu Zhu, Jianzhong Gu, J P Draayer, Xiaoguang Wu, Lihua Zhu, Chuangye He, Guangsheng Li, Beibei Yu, Tingdun Wen, Yupeng Yan, High Spin States and Level Structure in Rubidium-84, Phys. Rev. C82, (2010)014306 • [2]Dida Zhang, Zhongyu Ma, Baoqiu Chen, Shuifa Shen, Alpha-decay halflives of superheavy elements with the Dirac Brueckner-Hartree Fock (DBHF) nucleon effective interaction, Phys. Rev. C81, (2010)044319 (注：第一作者张地大(Dida Zhang)是我的硕士生) • [3]W.H. Zou, Y. Tian, J.Z. Gu, S.F. Shen, J.M. Yao, B.B. Peng, Z.Y. Ma, Microscopic description of nuclear structure around 80Zr, Phys. Rev. C(in press) (注：第一作者邹文华(W.H. Zou)是我的硕士生) • [4]S.F. Shen, T.D. Wen, S.J. Zheng, J.Z. Gu, H.L. Liu, Y.B. Chen, T.T. Wang, Triaxial shape in Os-Pt region from ground states to collective rotational states, Modern Physics Letters A25(2010)805 • [5]Xuzhong Kang, Shuifa Shen(通讯作者), Guangbing Han, Feng Pan, Jianzhong Gu, J P Draayer, Xiaoguang Wu, Lihua Zhu, Tingdun Wen, Study of the High Spin States in Stable Nucleus 84Sr, Sciences in China, G(in press) (注：第一作者康旭忠(Xuzhong Kang)是我的硕士生) • 第十届国际核－核碰撞会议文章： • [6]S.-F. Shen, F. Pan, J.-Z. Gu, L.-H. Zhu, X.-G. Wu, J. P. Draayer, T.-D. Wen, Low-spin states and level structure of odd-even rubidium isotope: 83Rb, Nuclear Physics A834, (2010) 90c • [7]J.-Z. Gu,B.-B. Peng, W.-H. Zou, S.-F. Shen, Decay out of a superdeformed band: chaoticity dependence and a microscopic understanding, Nuclear Physics A834, (2010) 87c