nucleon-pair transfer-intensities as a fingerprint for nuclear shape-phase transitions ruben fossion...

Nucleon-pair transfer-intensities

as a fingerprint for nuclear shape-phase

transitions

Ruben FossionIstituto Nazionale di Fisica Nucleare (INFN)

Università di PadovaITALY

INPC2007, Tokyo, Japan

Changing nuclear structure through a series of isotopesParadigms/benchmarks to understand nuclear structure

Pair breaking

Vibrator VibratorRotor

INFN, Università di Padova, Italy INPC2007, Tokyo, Japan Ruben Fossion

s.p. behaviour(shell model)

Pair breaking

s.p. behaviour(shell model)Collective behaviour

Geometrical model

Fig. from R. Casten “Nuclear Physics from a Simple Perspective”

x

Recently 2 new analytical solutions for the critical points X(5), E(5)•F. Iachello, PRL85 (2000) 3580•F. Iachello, PRL87 (2001) 052502

Nuclear shape-phase transitions

Interacting Boson Model (IBM)A. Arima and F. Iachello, “The Interacting Boson Model”, Cambridge University Press, 1987

• valence bosons as basic building blocks s (L=0) and d (L=2)

• algebraic structure U(6) with three limits that have exact analytical solutions for the excitation spectrum and the EM-transition rates

• outside of the limits only numerical solutions

IBM symmetry-triangle“phase diagram”

Boson coherent states/condensates• geometrical interpretation of the IBM

x

vibratorAxial

symmetric rotor

Axial asymmetric

rotor

Fig. from R. Casten and E. McCutchan, J. Phys. G34 (2007) R285


spherical

deformed

5. Transizioni di fase di forma: sistemi macroscopici

Discontinuities where the phase changes

Analogy with macroscopic systems


Search for fingerprints of nuclear shape-phase changesObservables• 2-neutron separation energies• B(E2,21

+ -> 01+)

• B(E0,02+ -> 01

+)• Isomer shift• R=E(41

+)/E(21+)

• Isotope shift• B(E2,22+ -> 01+) B(E2,22+ -> 21+)• Pair-transfer reaction intensities

Experiments on pair transfer• In the past: with stable beams• Renewed interest: experiments with exotic beams

D. Bucurescu, et. al., Phys. Rev. C73, 064309 (2006).D.A.Meyer et. al., Phys. Rev. C74, 044309 (2006).D.A. Meyer et. al., Phys. Lett. B638, 44 (2006).P. Van Duppen et al., the ISOLDE collaboration (CERN), internal communication.

Microscopic systems - Experimental observables


Can we learn something from pair-transfer reactions about nuclear shape-phase transitions and the critical points?

Fingerprints of shape-phase transitions in 2-particle transfer reactions

• Theoretically, if you move from one limit of nuclear structure to another, how will the intensity of the pair-transfer change. Can we identify fingerprints for shape transitions and critical points?

• Do we find these fingerprints back in real series of isotopes?


Fingerprints of shape-phase transitions in 2-particle transfer reactions1. From a spherical vibrator to an axial symmetric rotor


Experimental information on the 64Gd isotope series

150 154 158 162A

R. Casten and E.A. McCutchan, J. Phys. G34 (2007) R285

2. Some series of isotopes



Spherical vibrator

Axial symmetric

rotor

R. Fossion et al., accepted by Phys. Rev. C

Pick-upStrip-off

Α=154 Α=154


Conclusions• We suggest as a fingerprint for the critical point for nuclear phase-shape transitions a loss of intensity for the pair transfer between two ground states in combination with a gain of intensity for transfer to excited states

Collaborators• INFN, Padova, Italy A. Vitturi and L. Fortunato• Universidad de Sevilla, Spain C. Alonso and J. Arias

ありがとうございますThank you

Simple algebraic results in the Boson Coherent-State frameworkExpression of the nucleon-pair transfer intensity

in terms of the number of bosons and quadrupole deformation variables (N, β1, β2)

Ground-state to ground-state transfer

Transfer of the ground-state to the beta-vibrational state


N=15

β1

β1

β2

β2

R. Fossion et al., accepted by Phys. Rev. C

β1=β2

Pair-transfer intensities in the IBM-1

Definition of the operatorsMost general boson-equivalent of the L=0 pair-transfer operator P(0)

+,0 up to cubic terms

Operator cast into a more condensed form

In a first approximation, the transfer intensity can be defined as

Connection with experiments σ=(kinematics)×(structure)

1 1 1 1

1 διεγερμ. 1 διεγερμ.

0 0 1 0 0 1

0 0 1 0 0 1

N N N N

N N N N

I

I

AN bosons

gsγ

ββγγ βγ

β

γγ

Κ=0

Κ=0

Κ=0

Κ=2

Κ=2

Κ=0

Κ=4

A+2(N+1) bosons

gs

ββγγ βγ

γγ

Κ=0

Κ=0

Κ=0

Κ=2

Κ=0

Κ=2

Κ=4

β

γ

Boson analogue of the nucleon-pair transfer-operatorWithin the IBM

• algebraic results for the limits• numerical results between the limits

Boson Coherent-State frameworks• simple analytical formulae

s† (λ=0,μ=0)ΔL=0ΔK=0

0+ 0+

K=0 K=0

Transfer of an s-boson


Pair-transfer intensities, gs dbv in the three limits

Fingerprints of shape-phase transitions

Fase transition from a spherical vibrator to a axial asymetric deformed rotor

Fragmentation of the transfer strength

R. Casten and E.A. McCutchan, J. Phys. G34 (2007) R285D. Meyer et al., Phys. Lett. B638 (2006) 44.

Huge density of 0+ states near the critical point

IBM numerical calculation

New benchmarks: analytical solutions X(5) and E(5) for the critical points

Fig. from R. Casten, Nature

New benchmarks: analytical solutions X(5) and E(5) for the critical points

Fig. from R. Casten and E. McCutchan, J. Phys. G34 (2007) R285

F. Iachello, PRL85 (2000) 3580

F. Iachello, PRL87 (2001) 052502

First and second order shape-phase transitions in nuclei

nucleon-pair transfer-intensities as a fingerprint for nuclear shape-phase transitions ruben fossion...

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