Physics of neutron-rich nuclei

Transcription

1 Physics of neutron-rich nuclei Nuclear Physics: developed for stable nuclei (until the mid 1980 s) saturation, radii, binding energy, magic numbers and independent particle.

2 Physics of neutron-rich nuclei Nuclear Physics: developed for stable nuclei (until the mid 1980 s) - how many neutrons can be put into a nucleus when the number of proton is fixed? - what are the properties of nuclei far from the stability line?

3 Physics of neutron-rich nuclei characteristic features of nuclei close to the neutron-drip line?

4 Physics of unstable nuclei Unveil new properties of atomic nuclei by controlling the proton and neutron numbers Explore the new phases and dynamics of nuclear matter at several proton and neutron densities

5 New generation RI beam facility: RIKEN RIBF (Radioactive Isotope Beam Factory) a facility to create unstable nuclei with the world largest intensity physics of unstable nuclei the origin of elements superheavy nuclei

6 A start of a research on unstable nuclei: interaction cross sections (1985) Projectile Target Slide: A. Ozawa 11 Li nuclei other than 11 Li target nucleus if reaction takes place when overlap: R I (P) R I (T) R I (P) projectile target

7 A start of a research on unstable nuclei: interaction cross sections (1985) 11 Li nuclei other than 11 Li very large radius target nucleus R I (P) projectile target R I (T) I. Tanihata et al., PRL55( 85)2676 if reaction takes place when overlap: R I (P)

8 One neutron halo nuclei A typical example: 11 4Be 7 One neutron separation energy radius S n 10 Be + n 11 Be I. Tanihata et al., PRL55( 85)2676; PLB206( 88)592 S n = 504 +/- 6 kev very small cf. S n = 4.95 MeV for 13 C

9 One neutron halo nuclei A typical example: 11 4Be 7 One neutron separation energy radius 11 Be S n 10 Be + n S n = 504 +/- 6 kev very small Interpretation:a weakly bound neutron surrounding 10 Be 10 Be n weakly bound system large spatial extension of density (halo structure)

10 Interpretation:a weakly bound neutron surrounding 10 Be 10 Be n weakly bound system large spatial extension of density (halo structure) Density distribution which explains the experimental reaction cross section lunar halo (a thin ring around moon) M. Fukuda et al., PLB268( 91)339

11 Momentum distribution 8 He S 2n ~ 2.1 MeV 11 Li S 2n ~ 300 kev a narrow mom. distribution when weakly bound and thus a large spatial extension neutron halo T. Kobayashi et al., PRL60 ( 88) 2599

12 Properties of single-particle motion: bound state core n assume a 2body system with a core nucleus and a valence neutron core r n consider a spherical potential V(r) as a function of r cf. mean-field potential: Hamiltonian for the relative motion

13 core V(r) r n Hamiltonian for the relative motion For simplicity, let us ignore the spin-orbit interaction (the essence remains the same even if no spin-orbit interaction) Boundary condition for bound states * For a more consistent treatment, a modified spherical Bessel function has to be used

14 Angular momentum and halo phenomenon Centrifugal potential (enlargement) The height of centrifugal barrier: 0 MeV (l = 0), 0.69 MeV (l = 1), 2.94 MeV (l = 2)

15 Wave function Change V 0 for each l so that ε = -0.5 MeV l = 0 : a long tail l = 2 : localization l = 1 : intermediate root-mean-square radius 7.17 fm (l = 0) 5.17 fm (l = 1) 4.15 fm (l = 2)

16 Wave functions

17 Radius: diverges for l=0 and 1 in the zero energy limit Halo (a very large radius) happens only for l= 0 or 1

18 weakly bound e = MeV V 0 = 24 MeV R = fm a l=0 bound state in a square well pot. e = MeV V 0 = 10 MeV R = fm

19 Other candidates for 1n halo nuclei 19 C: S n = 0.58(9) MeV 31 Ne: S n = / MeV Large Coulomb breakup cross sections Coulomb breakup of 19 C T. Nakamura et al., PRL83( 99)1112 T. Nakamura et al., PRL103( 09)262501

20 Coulomb breakup of 1n halo nuclei A Z A Z * A-1 Z + n γ Transition from the g.s. to excited states by absorbing γ rays γ breakup if excited to continuum states excitations due to the Coulomb field from the target nucleus

21 Electromagnetic transitions photon k polarization vector (spin wave function of photon) initial state: final state: transition H int (interaction between a nucleus and EM field) State of nucleus: Ψ i, + one photon with momentum k, and polarization α ( α = 1 or 2)

22 Application to the present problem (in the dipole approximation): z n

23 Application to the present problem (in the dipole approximation): z n large transition probability if the spatial extention in z is large

24 Simple estimate of E1 strength distribution (analytic model) Transition from an l = 0 to an l = 1 states: WF for the initial state: WF for the final state: j 1 (kr) : spherical Bessel function The integral can be performed analytically Refs. (for more general l i and l f ) M.A. Nagarajan, S.M. Lenzi, A. Vitturi, Eur. Phys. J. A24( 05)63 S. Typel and G. Baur, NPA759( 05)247

25 Wigner-Eckart theorem and reduced transition probability Reduced transition probability

26 peak position: peak height: Total transition probability: a high and sharp peak as the bound state energy, E b, becomes small As the bound state energy, E b, gets small, the peak appears at a low energy E peak = 0.28 MeV (E b =-0.5 MeV) cf. MeV

27 Sum Rule Total E1 transition probability: proportional to the g.s. expectation value of r 2 If the initial state is l=0 or l=1, the radius increases forweakly bound Enhancement of total E1 prob. Inversely, if a large E1 prob. (or a large Coul. b.u. cross sections) are observed, this indicates l=0 or l=1 halo structure

28 Other candidates for 1n halo nuclei 19 C: S n = 0.58(9) MeV 31 Ne: S n = / MeV Large Coulomb breakup cross sections Coulomb breakup of 19 C T. Nakamura et al., PRL83( 99)1112 T. Nakamura et al., PRL103( 09)262501

29 Deformed halo nucleus 31 Ne 20 1f 7/2 1d 3/2 2s 1/2 1d 5/2 1p 1/2 1p 3/2 1s 1/2 T. Nakamura et al., PRL103( 09) Ne 21 large Coulomb break-up cross sections halo structure? spherical potential no halo (f-wave) deformation?

30 Nilsson model analysis [I. Hamamoto, PRC81( 10)021304(R)] f 7/2 β=0.3 21st neutron p 3/2 β=0.5 f 7/2 non-halo (Ω π = 3/2 + ) p 3/2

31 31 Ne T. Nakamura et al., PRL103( 09) large Coulomb break-up cross sections E 2+ ( 30 Ne) = 0.801(7) MeV P. Doornenbal et al., PRL103( 09) S n ( 31 Ne) = / MeV Y. Urata, K.H., and H. Sagawa, PRC83( 11)041303(R)

32 2n halo nucleus

33 Three-body model : microscopic understanding of di-neutron correlation 11 Li, 6 He n r 1 core r 2 n (the last term: the recoil kinetic energy of the core nucleus in the three-body rest frame) Obtain the ground state of this three-body Hamiltonian and investigate the density distribution (e.g.,) expand the wf with the eigen-functions for H without V nn and determine the expansion coefficients

34 Comparison between with and without paring correlations 11 Li a distribution of one of the neutrons when the other neutron is at (z 1, x 1 )=(3.4 fm, 0) Without pairing [1p 1/2 ] 2 With pairing When no pairing, symmetric between z and z. The distribution does not change whereever the 2nd neutron is. When with pairing, the nearside density is enhanced. The distribution changes when the 2nd neutron moves.

35 What is Di-neutron correlation? Correlation: Example: 18 O = 16 O + n + n cf. 16 O + n : 3 bound states (1d 5/2, 2s 1/2, 1d 3/2 ) i) Without nn interaction: Distribution of the 2 nd neutron when the 1 st neutron is at z 1 : z 1 = 1 fm z 1 = 2 fm z 1 = 3 fm z 1 = 4 fm Two neutrons move independently No influence of the 2 nd neutron from the 1 st neutron

36 What is Di-neutron correlation? Correlation: Example: 18 O = 16 O + n + n cf. 16 O + n : 3 bound states (1d 5/2, 2s 1/2, 1d 3/2 ) ii) nn interaction: works only on the positive parity (bound) states z 1 = 1 fm z 1 = 2 fm z 1 = 3 fm z 1 = 4 fm distribution changes according to the 1 st neutron (nn correlation) but, the distribution of the 2 nd neutron has peaks both at z 1 and z 1 this is NOT called the di-neutron correlation

37 What is Di-neutron correlation? Correlation: Example: 18 O = 16 O + n + n cf. 16 O + n : 3 bound states (1d 5/2, 2s 1/2, 1d 3/2 ) ii) nn interaction: works only on the positive parity (bound) states 0 +,2 +,4 +,6 +, z 1 = 3 fm 0 + pairing correlation does not necessarily lead to a compact configuration (when the model space is stricted)

38 What is Di-neutron correlation? Correlation: Example: 18 O = 16 O + n + n cf. 16 O + n : 3 bound states (1d 5/2, 2s 1/2, 1d 3/2 ) iii) nn interaction: works also on the continuum states z 1 = 1 fm z 1 = 2 fm z 1 = 3 fm z 1 = 4 fm spatial correlation: the density of the 2 nd neutron localized close to the 1 st neutron (dineutron correlation) parity mixing: essential role cf. F. Catara et al., PRC29( 84)1091

39 Example: 18 O = 16 O + n + n cf. 16 O + n : 3 b.s.(1d 5/2, 2s 1/2, 1d 3/2 ) i) positive parity only insufficient z 1 = 1 fm z 1 = 2 fm z 1 = 3 fm z 1 = 4 fm ii) positive + negative parities (bound + continuum states)

40 Recent topic: two-neutron decay of unbound 26 O nucleus 17 F 18 F 19 F 20 F 21 F 22 F 23 F 24 F 25 F 26 F 27 F 29 F 31 F 13 O 14 O 15 O 16 O 17 O 18 O 19 O 20 O 21 O 22 O 23 O 24 O 12 N 13 N 14 N 15 N 16 N 17 N 18 N 19 N 20 N 21 N 22 N 23 N 9 C 10 C 11 C 12 C 13 C 14 C 15 C 16 C 17 C 18 C 19 C 20 C 22 C 22 O 23 O 24 O 25 O 26 O 26 O 24 O + n + n Expt. : 27 F 26 O 24 O + n + n MSU: E. Lunderberg et al., PRL108 ( 12) GSI: C. Caesar et al., PRC88 ( 13) RIKEN: Y. Kondo et al., PRL116( 16)102503

41 Experimental data for decay spectrum Expt. : 27 F 26 O 24 O + n + n MSU: E. Lunderberg et al., PRL108 ( 12) GSI: C. Caesar et al., PRC88 ( 13) RIKEN: Y. Kondo et al., PRL116( 16) kev 25 O 2n decay 18 kev 24 O 26 O Y. Kondo et al., PRL116( 16)102503

42 Decay energy spectrum three-body model calculations with nn interaction K.H. and H. Sagawa, - PRC89 ( 14) PRC93( 16) O without nn interaction d 3/2 3/ O 25 O 749 kev 26 O 18 kev E peak = 18 kev Data: Y. Kondo et al., PRL116( 16)102503

43 Decay energy spectrum K.H. and H. Sagawa, - PRC89 ( 14) PRC93( 16) O MeV 0 + 3/ O 749 kev kev 24 O 26 O a prominent second peak at E = MeV Data: Y. Kondo et al., PRL116( 16)102503

44 a textbook example of pairing interaction! [jj] (I) = 0 +,2 +,4 +,6 +,.. w/o residual interaction (MeV) (d 3/2 ) (0.418) O dineutron correlation 0 + with residual interaction 0 +

45 Decay of unbound nuclei beyond the drip lines.as a probe for di-neutron correlations inside nuclei 11 Li How to probe it? Coulomb breakup disturbance due to E1 field two-proton decays two-neutron decays spontaneous emission without a disturbance K.H. and H. Sagawa, PRC72 ( 05) B. Blank and M. Ploszajczak, Rep. Prog. Phys. 71( 08)046301