Configuration interaction studies of pairing and clustering in light nuclei

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1 Configuration interaction studies of pairing and clustering in light nuclei Alexander Volya Florida State University DOE support: DE-SC9883 Trento September 216

2 Questions Description of clustering, from theory to experiment Geometric structure of alpha clusters, real vs algebraic structures Interplay between pairing and clustering

3 Cluster-nucleon configuration interaction approach Traditional shell model configuration m-scheme Cluster configuration SU(3)-symmetry basis i = i a 1 a 2...a A i channeli = A { D} i Di D i Di Boosts, m-scheme, and SU(3) basis Construction and classification of cluster configurations Center of mass and translational invariance Non-orthogonality and bosonic principle

4 Center-of-Mass (CM) boosts Shell model, Glockner-Lawson procedure and CM quanta creation and annihilation (vectors) Intrinsic SM state Center-of-mass state motion CM angular momentum operator 1s d p R s Select configuration content of NCSM wave functions for 4He with Ω = 2 MeV boosted by 8 quanta (L = ). K Kravvaris and A. Volya, Journal of Physics: Conference Series, Cluster 216, Napoli.

5 Cluster configurations Volya and Yu. M. Tchuvil sky, Phys. Rev. C 91, (215). Yu. F. Smirnov and Yu. M. Tchuvil sky, Phys. Rev. C 15, 84 (1977). M. Ichimura, A. Arima, E. C. Halbert, and T. Terasawa, Nucl. Phys. A 24, 225 (1973). O. F. Nemetz, V. G. Neudatchin, A. T. Rudchik, Yu. F. Smirnov, and Yu. M. Tchuvil sky, Nucleon Clusters in Atomic Nuclei and Multi-Nucleon Transfer Reactions (Naukova Dumka, Kiev, 1988), p Example: alpha decay with ll= from sd shell 21 way to make L= T= 4-nucleon combination Each nucleon has 2 oscillator quanta, 8 quanta total In oscillator basis excitation quanta are conserved We model alpha as 4-nucleons on s-shell (s) 4 Make single SU(3) operator with quantum numbers (8,) Cluster coefficient is known analytically X n ` 1s d (8,):`m p s R n`m(1) n`m (2) n`m (3) n`m (4) {z } 4 2=8 quanta m-scheme state $ X X n ` SU(3) symmetry state (8,):`m = n `m (R ) {z } 8quanta motion of alpha {z} quanta

6 Center-of-mass recoil correction Channel of relative motion 2 1 n 2`2 n 1`1

7 Translational invariance from recoil Shell model, Glockner-Lawson procedure Intrinsic SM state Center-of-mass state vibration Factorizing center of mass in overlap integral SM overlap integral (FPC) Translationally invariant part Spurious CM integral Recoil factor (inverse of Talmi-Moshinsky coefficient)

8 Traditional Cluster Spectroscopic Characteristics = h D i Recoil Factor Cluster Coefficient Fractional Parentage Coefficient Traditional old spectroscopic factors Expand radial motion in HO wave functions

known analytically 64/45 Effective operators (alphas) are not

9 If Bosonic nature of 4-nucleon operators non-orgothogonality is thought of as being a boson then * For p-shell the result is known analytically 64/45 Effective operators (alphas) are not ideal bosons Cluster configurations are not orthogonal and not normalized

10 Orthogonality condition model, new SF Non-orthogonal set of channels (over-complete set of configurations) Pauli exclusion principle Matching procedure, asymptotic normalization, connection to observables No agreement with experiment on absolute scale Resonating group method New spectroscopic factor Sum of all new SF from all parent states to a given final state equals to the number of channels R. Id Betan and W. Nazarewicz Phys. Rev. C 86, (212) S. G. Kadmenskya, S. D. Kurgalina, and Yu. M. Tchuvil sky Phys. Part. Nucl., 38, (27). R. Lovas et al. Phys. Rep. 294, No. 5 (1998) T. Fliessbach and H. J. Mang, Nucl. Phys. A 263, (1976). H. Feschbach et al. Ann. Phys. 41 (1967)

Alpha clustering in sd-shell nuclei USDB interaction [5] (8,) configuration Old SF are small Old SF decrease with A [1] T. Carey, P. Roos, N. Chant, A. Nadasen, and H. L. Chen, Phys. Rev.

11 Alpha clustering in sd-shell nuclei USDB interaction [5] (8,) configuration Old SF are small Old SF decrease with A [1] T. Carey, P. Roos, N. Chant, A. Nadasen, and H. L. Chen, Phys. Rev. C 23, 576(R) (1981). [2] T. Carey, P. Roos, N. Chant, A. Nadasen, and H. L. Chen, Phys. Rev. C 29, 1273 (1984). [3] N. Anantaraman and et al., Phys. Rev. Lett. 35, 1131 (1975). [4] W. Chung, J. van Hienen, B. H. Wildenthal, and C. L. Bennett, Phys. Lett. B 79, 381 (1978). [5] B. A. Brown and W. A. Richter, Phys. Rev. C 74, (26)

13 SF Alpha cluster spectroscopic factors in 24 Mg SF 1-1 Theoretical calculations in SD shell 1 L= L=2 21 Experimental results E. S. Diffenderfer, et.al Phys. Rev. C 85, (212). SF L= L=6 SF SF L=8 Rotational Structures E [MeV] The sd valence space is considered with USDB interaction the operator is

14 Building cluster channels with realistic alpha SD-shell nuclei Effective sd-shell interaction USDB JISP interaction SF.6 SF N max = N max =2 N max =4 N max = N max = N max =2 N max =4 N max = A A

15 Excitation Energy [MeV] p-sd shell model SU(3) configurations For positive parity Hamiltonian from E. K. Warburton and B. A. Brown, Phys. Rev. C 46 (1992) 923 Y. Utsuno and S. Chiba, Phys. Rev. C (R) (211) Spectroscopic factor.9 1Experiment Theory (new) S

16 Rotational structure in 16 O 6 5 exp SM J(J1) Full p-sd shell calculations, included operators are SF(alpha).2.1 Yamada* (1).6.8 (2).8.54 (3).2.22 This Work * Yamada, et. al Clusters in nuclei, Vol 2, (Springer-Verlag, 212) page p-sd shell model calculation p-sd effective 6 hamiltonian E. K. Warburton 5 and B. A. Brown, Phys. Rev. C 46 (1992) 923 Y. Utsuno and S. Chiba, Phys. Rev. C (R) (211) B(E2) Ex [MeV]

Excitation Energy [MeV] 6 2 6-2 5 1 16 6 1-5 1 6 1 14 3 4 2 4 1 2 2-1 2-1 1 2 1-3 1 2 4 2 2 3 3 4 1

17 Excitation Energy [MeV] Experiment Theory Spectroscopic factor (new) S

18 28 Si 48 Cr SF SF pairing strength pairing strength

Classic Example: 24 Mg, 8 nucleons in sd-shell (8,4)

(4,6) (1,) (1,6) (,5) (,8) (8,1) (7,3) (8,4) (7,)

(6,2) (3,5) (4,) (5,1) (,2) (6,2) (4,3) (2,1) (1,3)

19 Classic Example: 24 Mg, 8 nucleons in sd-shell (8,4) Realistic (6,2) (9,2) (5,1) (7,3) (8,1) (7,) (1,) (4,6) (1,) (1,6) (,5) (,8) (8,1) (7,3) (8,4) (7,) Pairing (T=1) Random (2,4) (9,2) (1,) (7,) (2,7) (8,1) (7,3) (4,6) (3,2) (8,4) (6,5) (1,6) (,5) (,8) (3,5) (2,4) (4,) (3,2) (1,3) (2,1) (5,1) (,2) (4,3) (6,2) (3,5) (4,) (5,1) (,2) (6,2) (4,3) (2,1) (1,3) USD realistic interaction Ground state J=T= breakdown in SU(3) irreps

pairing (λ T= ); three plots indicate phase diagram as a function of

20 24 Mg phase diagram Contour plot of invariant correlational entropy showing a phase diagram as a function of T=1 pairing (λ T=1 ) and T= pairing (λ T= ); three plots indicate phase diagram as a function of non-pairing matrix elements (λ np ). Realistic case is λ T=1 =λ T= =λ np =1

21 Invariant Correlational Entropy Parameter-driven equilibration (pairing strength) Averaged density matrix ICE Advantages Basis independent Explore individual quantum states Needs no heat bath No equilibration, thermalization and particle number conservation issues. Probe sensitivity of states to noise in external parameter(s) Phase transitions -> peaks in ICE

22 24 Mg phase transitions

23 How deformation can enhance paring. Quadrupole-quadrupole interaction on single j-level Exchange terms result in attractive pairing interaction Terms scale as 1/Ω where Ω=2j1 Pairing is the strongest particle-particle interactions A. Volya, Phys. Rev. C. 65, (22)

24 Acknowledgements: Thanks to: K. Kravvaris, V. Zelevinsky, Yu. Tchuvil sky, J. Vary, T Dytrych Funding: U.S. DOE contract DE-SC9883. Publications: K Kravvaris and A. Volya, Journal of Physics: Conference Series, Cluster 216, Napoli. A. Volya and Y. M. Tchuvil'sky, Phys.Rev.C 91, (215); J. Phys. Conf. Ser. 569, 1254 (214); (World Scientific, 214), p M. L. Avila, G. V. Rogachev, V. Z. Goldberg, E. D. Johnson, K. W. Kemper, Y. M. Tchuvil'sky, and A. Volya, Phys. Rev. C 9, (214). A. Volya, Phys. Rev. C. 65, (22) A. Volya and V. Zelevinsky, Phys. Lett. B574, (23)

Configuration interaction approach to nuclear clustering

Configuration interaction approach to nuclear clustering Alexander Volya Florida State University Configuration interaction approach A powerful tool in studies of nuclear many-body problems De-facto most