Reassessing the Vibrational Nuclear Structure of 112 Cd

Transcription

1 Reassessing the Vibrational Nuclear Structure of 112 Cd February 212

2 1 Vibrational Nuclear Structure Nuclear Vibrations in the Collective Model Vibrational Structure of the 112 Cd Sources of Inconsistency in the Vibrational Interpretation 2 Experiment and Analysis Maier-Leibnitz Laboratory and the Q3D 112 Cd spectrum from the d,p reaction DWBA Calculations and Spectroscopic Factors 3 Preliminary Results Transfer Angular Distributions DWBA Transfer Angular Distributions ADWA Reassignment and the Quadrupole-Octupole States

3 Nuclear Vibrations in the Collective Model

4 Nuclear Vibrations in the Collective Model The Nucleus is treated as a spherical liquid drop

5 Nuclear Vibrations in the Collective Model The Nucleus is treated as a spherical liquid drop Vibrational excitations occur on the nuclear surface: λ R(t) = R av + a λµ (t)y λµ (θ, φ) λ= µ= λ

6 Nuclear Vibrations in the Collective Model The Nucleus is treated as a spherical liquid drop Vibrational excitations occur on the nuclear surface: R(t) = R av + λ λ= µ= λ a λµ (t)y λµ (θ, φ) The λ = mode is a monopole vibration, which is purely radial

7 Nuclear Vibrations in the Collective Model The Nucleus is treated as a spherical liquid drop Vibrational excitations occur on the nuclear surface: R(t) = R av + λ λ= µ= λ a λµ (t)y λµ (θ, φ) The λ = mode is a monopole vibration, which is purely radial The λ = 1 mode is a dipole vibration, which corresponds to shifts in the nuclear centre of mass

8 Vibration in the 112 Cd Quadrupole-Octupole Vibrational Spectrum 4ω 3ω 2ω ω 2 + +

9 Vibration in the 112 Cd Quadrupole-Octupole Vibrational Spectrum 4ω 3ω 2ω ω 2 + +

10 Vibration in the 112 Cd Quadrupole-Octupole Vibrational Spectrum 4ω 3ω ω ω 2 + +

11 Vibration in the 112 Cd Quadrupole-Octupole Vibrational Spectrum 4ω 3ω ω ω 2 + +

12 Vibration in the 112 Cd Quadrupole-Octupole Vibrational Spectrum 4ω ω ω ω 2 + +

13 Vibration in the 112 Cd Quadrupole-Octupole Vibrational Spectrum Spectrum of low-lying states in 112 Cd 4ω ω ω ω

14 Sources of Inconsistency in the Vibrational Interpretation There is more to nuclear structure than the energy spacings, and spin-parity assignments of excited states

15 Sources of Inconsistency in the Vibrational Interpretation There is more to nuclear structure than the energy spacings, and spin-parity assignments of excited states branching ratios lifetimes composition of wave-functions

16 Sources of Inconsistency in the Vibrational Interpretation There is more to nuclear structure than the energy spacings, and spin-parity assignments of excited states branching ratios lifetimes composition of wave-functions Using the 111 Cd( d,p) 112 Cd reaction, single-particle component of states in 112 Cd can be measured populate states in 112 Cd through single neutron transfer

17 Maier-Leibnitz Laboratory and the Q3D Multipole Dipole 2 Polarized deuterons accelerated to 22 MeV with a tandem Van de Graaff accelerator Dipole 1 Quadrupole Dipole 3 Focal plane 111 Cd Target d beam Faraday cup E E position sensitive cathode-strip detector (particle ID + energy)

18 Maier-Leibnitz Laboratory and the Q3D Multipole Dipole 2 Polarized deuterons accelerated to 22 MeV with a tandem Van de Graaff accelerator 8% polarization was achieved Dipole 1 Quadrupole 111 Cd Target d beam Dipole 3 Focal plane Faraday cup E E position sensitive cathode-strip detector (particle ID + energy)

19 Maier-Leibnitz Laboratory and the Q3D Multipole Dipole 2 Polarized deuterons accelerated to 22 MeV with a tandem Van de Graaff accelerator 8% polarization was achieved Deuteron beam was incident on a 15 µg/cm 2 target of 111 Cd Dipole 1 Quadrupole 111 Cd Target d beam Dipole 3 Focal plane Faraday cup E E position sensitive cathode-strip detector (particle ID + energy)

20 Maier-Leibnitz Laboratory and the Q3D Outgoing protons detected with Q3D magnetic spectrometer Multipole Dipole 2 Polarized deuterons accelerated to 22 MeV with a tandem Van de Graaff accelerator 8% polarization was achieved Deuteron beam was incident on a 15 µg/cm 2 target of 111 Cd Dipole 1 Quadrupole 111 Cd Target d beam Dipole 3 Focal plane Faraday cup E E position sensitive cathode-strip detector (particle ID + energy)

21 Maier-Leibnitz Laboratory and the Q3D Outgoing protons detected with Q3D magnetic spectrometer Elastic scattering data and ( d, p) transfer data were collected at angles between 1 and 6 Multipole Dipole 2 Polarized deuterons accelerated to 22 MeV with a tandem Van de Graaff accelerator 8% polarization was achieved Deuteron beam was incident on a 15 µg/cm 2 target of 111 Cd Dipole 1 Quadrupole 111 Cd Target d beam Dipole 3 Focal plane Faraday cup E E position sensitive cathode-strip detector (particle ID + energy)

22 112 Cd Spectrum from the d,p reaction Low excitation energy from kev to 238 kev at 2 with beam polarization up Counts GS, + 617, 2 + The 2373 kev 5 state assigned as a quadrupole-octupole state is strongly populated in this reaction, it is one of the largest peaks in the spectrum Channel Number 1224, , , , , + 25, 3-282, , , , , , 5 -

23 112 Cd Spectrum from the d,p reaction High excitation energy from 2 kev to 43 kev at 4 with beam polarization up , , 5-318, Counts , + 256, , , , , , , Channel Number 2894, , 4-32, , , , , , , (3-5) 3557, 3-374, , , 4 +

24 DWBA Calculations and Spectroscopic Factors Distorted-Wave Born Approximation calculations are performed and compared to the experimental data U = U bind + U int Interactions with nuclear volume are given by a Wood-Saxon potential Surface-dominated interactions are given by the derivative of a Wood-Saxon potential 1 U v = V r 1 exp( r Rr ) + 1 iwv a r 1 exp( r R i ( ) d 1 U s = i4a i W s dr 1 exp( r R i ) a i ( ) λ 2 π d 1 U so = V so l s r so dr 1 exp( r Rso ) a so a i )

25 Transfer Angular Distributions DWBA 1 1 dσ dω cm [ µb ] sr 2834KeV l=.4 j=1/2 A y 1 dσ dω cm [ µb ] sr 2962KeV l=3.1 j=7/2 A y KeV l=2.4.2 j=3/2 1 32KeV l=4.8.4 j=7/ KeV l=2.2 j=5/ KeV l=5.2 j=11/ θ cm dσ dσ = S lj dω EXP dω DWBA θ cm Deuteron OMPs: Bojowald et al. (1988) Proton OMPs: Becchetti and Greenlees (1968)

26 Transfer Angular Distributions ADWA There is another approximation scheme available for ( d, p) reactions

27 Transfer Angular Distributions ADWA There is another approximation scheme available for ( d, p) reactions The adiabatic approximation has the form of an optical-model calculation

28 Transfer Angular Distributions ADWA There is another approximation scheme available for ( d, p) reactions The adiabatic approximation has the form of an optical-model calculation The optical model potential for the adiabatic calculation is the sum of a proton and neutron potential, evaluated at half the deuteron energy

29 Transfer Angular Distributions ADWA 1 1 dσ dω cm [ µb sr ] 2834KeV l=.4 j=1/2 A y 1 dσ dω cm [ µb sr ] 2962KeV l=3.1 j=7/2 A y KeV l=2.4.2 j=3/2 1 32KeV l=4.8.4 j=7/ KeV l=2.2 j=5/ KeV l=5.2 j=11/ θ cm θ cm Varner et al. (1991) Deuteron OMPs: Bojowald et al. (1988) Proton OMPs: Becchetti and Greenlees (1968)

30 Reassignment and the Quadrupole-Octupole States 2373 kev kev 6 The 2373 kev, 5 state previously assigned to the quadrupole-octupole quintuplet shows strong 1h 11 2 characteristics θ cm Varner et al. (1991)

31 Reassignment and the Quadrupole-Octupole States The 2373 kev, 5 state previously assigned to the quadrupole-octupole quintuplet shows strong 1h 11 2 characteristics The 2817 kev 6 state also shows strong 1h 11 characteristics kev kev θ cm Varner et al. (1991)

32 Reassignment and the Quadrupole-Octupole States The 2373 kev, 5 state previously assigned to the quadrupole-octupole quintuplet shows strong 1h 11 2 characteristics The 2817 kev 6 state also shows strong 1h 11 characteristics kev kev both of these 5 and 6 states are strongly populated in this single neutron transfer reactions θ cm Varner et al. (1991)

33 Reassignment and the Quadrupole-Octupole States The 2373 kev, 5 state previously assigned to the quadrupole-octupole quintuplet shows strong 1h 11 2 characteristics The 2817 kev 6 state also shows strong 1h 11 characteristics kev kev both of these 5 and 6 states are strongly populated in this single neutron transfer reactions.1 this data suggests the wavefunctions of these two states are dominated by a 3s 1 2 1h 11 2 configuration Varner et al. (1991) θ cm

34 Summary Born approximation, with global OMPs does not reproduce the angular distributions and analyzing powers of the 111 Cd( d, p) 112 Cd reaction well Adiabatic approximation gives improved reproduction of the data, compared with DWBA A systematic comparrison of spectroscopic factors obtained from AWDA and DWBA calculations will be made A strong population of the 5 state previously assigned to the quadrupole-octupole quintuplet demonstrates a large single-particle component in the wavefunction, which is at odds with the assignment of this state within the vibrational model. Once spectroscopic strengths are obtained for each populated state, a reinterpretation of the vibrational spectrum of 112 Cd will need to be made on the basis of the single particle components of the observed states

35 Acknowledgements Advisor: P.E. Garrett Collaborators: Guelph G.A. Demand P. Finlay K.L. Green K.G. Leach A.A. Phillips C.S. Sumithrarachchi C.E. Svensson J. Wong TRIUMF G.C. Ball S. Triambak MLL-LMU R. Hertenberger H.-F. Wirth R. Krücken T. Faestermann

36 Deuteron Elastic Scattering on 111 Cd Deuteron global optical model parameter sets (OMPs) reproduce the 111 Cd( d, d ) 111 Cd angular distribution of elastic cross-sections and analyzing powers ] [ µb sr 1e+8 1e+6 Bucurescu et. al (25) [1] Bojowald et al. (26) [2] Daehnick, Childs and Vrcelj (198) [3] An and Cai (26) [4] The OMPs are used in distorted-wave Born approximation (DWBA) calculations with the DWUCK4 code The experimental elastic cross-sections are scaled to the DWBA calculation for a determination of the target thickness, which is crucial for obtaining correct angular distributions DWBA calculations performed using the DWUCK4 code for elastic scattering that reproduced the data best were from Bojowald et al. (1988) [2] dσcm dωcm A y = 3P 2 dσ dσ dω dω dσ dω + dσ dω θ cm

37 Ex (KeV) S lj ADWA S lj DWBA %-diff