From Nuclear Vibrations to Rotations as a Function of Spin Paddy Regan Dept. of Physics, University of Surrey, Guildford, GU2 7XH, UK e-mail: firstname.lastname@example.org
Main physics question, how is spin generated in the nucleus ? and related to this Are nuclei (with Z=40-50) Rotating or Vibrating ? * Signatures of vibrator-rotor structural evolution. * 102 Ru * an excellent ‘E-GOS’ example. * Odd-A cases; N=57 isotones 99 Mo, 101 Ru *, 103 Pd, 105 Cd * Future work, lifetime measurements * = Experiment performed at WNSL-Yale. Outline
Date: Mon, 16 Sep 1996 23:03:57 +0100 From: Con Beausang email@example.com To: P.Regan@firstname.lastname@example.org Hi Paddy, Greetings from the colonies (i know that this came from Liverpool but that’s because the primitive Yanks haven't got mail up on the new system yet.... give them time. Anyway I hope that we can do things together here. Let me tell you what we have or hope to have setup and running sometime....Ge detectors: We will have a variety adding up to a total of around 30 detectors. These comprise a mixed bag of detectors some better than others probably and coming from a variety of sources. Yale: 4-5 25%ish plus 5 70-80%ish plus plus 4 leps and coming from.....Rochester 8 25%ish On a longer term I have money to build (or start to build) a inner charged particle ball for p and alpha discrimination etc. There are also a variety of devices that one stumbles across including a plunger (perhaps of somewhat dubious character). The accelerator runs well to all accounts and beam time should be plentiful. Obviously not all the bits for the Ge array exist right now, which perhaps makes it a good time to start collaborations going. At the moment we (I) an trying to figure out a geometry that will suit the variety of detectors we will have in the short term and also the longer term upgradeability. Anyway drop me a line with your thoughts etc. All the best Con
Date: Tue, 21 Sep 1999 11:35:52 +0100 (BST) From: Miss Heather Newman To: email@example.com Subject: M Phys Placements Dear Dr. Regan, I was wondering if you happened to have any additional information on the placement that I have applied for at Yale. Perhaps I could arrange to pop by and talk about it with you later on in the week? Thanks Heather Newman
Date: Thu, 23 Sep 1999 16:41:06 +0100 (BST) From: Dr Patrick H Regan To: firstname.lastname@example.org Cc: a.clough, email@example.com Subject: Re: M Phys Placements Hi Heather, can you mail Prof. Con Beausang at Yale to `touch base' re. your placement there. I spoke to him today on the phone and he is looking forward to you going there. He is starting the paperwork which needs to be done (you need something called an IAP66 form to get a J-1 visa before they'll let you into the US!) Anyway mail Con on firstname.lastname@example.org so he knows who you are...email@example.com he's a very nice man! cheers Paddy
Subject: Visiting Staff Date: Tue, 15 Oct 2002 10:38:31 +0100 From: E.Herbert@surrey.ac.uk To: J.Tostevin@surrey.ac.uk Dear Prof. Tostevin, For information, earlier this morning the Visiting Staff Appointments Committee approved Professor Cornelius Beausang's appointment of Visiting Reader with effect from 1st September 2002. A letter will be sent to him in due course. Beth Herbert PA to Professor Bernard L Weiss, Head of School
22 V 22 EnEn n=0 n=1 n=2 n=3 http://npl.kyy.nitech.ac.jp/~arita/vib What do we mean by vibrating or rotating nuclei ?
Nuclear Rotations and Vibrations What are the signatures (in even-even nuclei) ? –(extreme) theoretical limits
Other signs of extreme rotation…. Coriolis-induced backbending. e.g., 135,7 Pm, C.W.Beausang et al., Phys. Rev. C36 (1987) p602
Sr-Mo region ‘famous’ for dramatic collapse in I =2 + energy going from N=58 to N=60
Explanation by Federman & Pittel in terms of quadrupole deformation ‘driving’ T=0 (pn) interaction. Particularly noticeable for protons and neutron orbitals with large spatial overlaps (e.g., Spin Orbit Partners such as g 9/2 and g 7/2 in A~100)
Other aspects ? Correlation between deformation & population of ‘deformation aligned’, low- h 11/2 neutron intruder orbitals. Classic ‘chicken and egg’. Does population of orbital ‘cause’ deformation or is deformation there from the core and thus h 11/2 orbital lies closer to the Fermi Surface ? How does this situation evolve with spin ?
Alignments and rotational motion in ‘vibrational’ 106 Cd (Z=48, N=58), PHR et al. Nucl. Phys. A586 (1995) p351
Can subtract off a reference (core) aligned angular momentum to see effect of quasi-particle alignments as a function of frequency. i x =5h CSM ref. Bengtsson Frauendorf and May, At. Data. Nuc. Data. Tab. 35 (1986) p15
Alignment (in the rotational picture) driven by Coriolis interaction on high-j, low- orbitals (ie. ones with large j x on collective rotation axis. V cor = -j x. eg. h 11/2 1/2 ‘intruder’ FS for N~57, 2 ~0.15->0.2 jxjx 50 82 1/2 - 1h 11/2 1g 9/2 3/2 -
Ru (Z=44) in the centre of the ‘deformed’ region for N=56-58 Anharmonic vibrator for the ground state ‘band’ is the usual explanation for 100 Ru and neighbours....but mid-shell (Z=40-50) nature is consistent with largest collectivity in the region. Q.Are these nuclei deformed or vibrational ? RuMoZrPdCdSn
Experimental Details (Jan. 2002) 96 Zr ( 9 Be,3n) 102 Ru, pace ~100mb 96 Zr( 9 Be,4n) 101 Ru, pace ~800mb Enriched (85%) 670 g/cm 2 96 Zr foil on 5mg/cm 2 nat Pb support. E beam =44 MeV, l max ~25 h YRASTBALL array at WNSL 6 clover germaniums @ 90 o 5 co-axial detectors @ 50 o + 126 o 3 co-axial detectors @ 160 o see Yamamoto, PHR, Beausang et al., Phys. Rev. C66 (2002)024302
PHR, Beausang, Zamfir, Casten et al., Phys. Rev. Lett. 90 (2002) 152502
If we parameterize with (E / J) vs. J Can see if rotor or vibrator by inspection
PHR, Beausang, Zamfir, Casten, Zhang et al., Phys. Rev. Lett. 90 (2003) 152502
E-GOS plot appears to indicate that Vibrator- Rotator phase change is a feature of near stable (green) A~100 nuclei. BUT….what is the microscopic basis ? ‘Rotational alignment’ can be a crossing between quasi- vibrational GSB & deformed rotational sequence. (stiffening of potential by population of high-j, equatorial (h 11/2 ) orbitals). PHR, Beausang, Zamfir, Casten, Zhang et al., Phys. Rev. Lett. 90 (2003) 152502
Q. Are backbends necessarily due to rotational alignment ? A. NO ! Can be vibrational – rotational structure change!!
E-GOS for other regions ? Z ~90 ? rotor vibrator
( h 11/2 ) 2 alignment in A~130 region appears to have analogous behaviour to ( h 11/2 ) 2 alignment in A~100 region. Conclusion? In many cases, ‘rotational alignment’ is actually a crossing between a quasi-vibrational ground state configuration and a deformed rotational sequence caused by stiffening of potential by population of high-j, equatorial (h 11/2 ) orbitals
Detailed spectroscopy allowed by investigating gamma-decay sequences from high-spin states. YRASTBALL used to identify band-like structures in N=57, 101 Ru. Yamamoto, PHR, Beausang et al., Phys. Rev. C66 (2002) 024302
Quasi-particle alignments and kinematic moments of inertia i x =10 h 11/2 band h 11/2 band N=57, intruder h 11/2 bands
TRS calculations for 101 Ru by F.R. Xu (Bejing) for different parity (and signature) configs. 22 =0.2MeV =0.4MeV =0.3MeV =0.6MeV Yamamoto, PHR, Beausang et al., Phys. Rev. C66 (2002) 024302
PROBLEM: Fusion-evaporation reactions can’t study high- spin states (and thus vibrational-rotational transitions, alignments etc.) in stable and neutron-rich systems such as next N=57 isotone, 99 Mo. SOLUTION: Use multi-nucleon transfer (DIC) reactions. Z N E beam ~15-20% above Coulomb barrier beam target (i) (ii) (iii)
See PHR, Yamamoto, Beausang, Zamfir, Casten, Zhang et al., AIP Conf. Proc. 656 (2002) p422 ‘Weak Coupling’ E /(I-j) E-GOS extension for odd-A Suggests 11/2 - band is an anharmonic vibrator or -soft rotor? seems to work ok for +ve parity bands though
Carl Wheldon (HMI-Berlin) has suggested extension of E-GOS by ‘renormalising’ the rotational energies at the bandhead. If the band-head spin of a sequence is given by j then substituting I j in place of I, one obtains,
seems to work ok, h 11/2 bands now look like rotors, Even-Even yrast sequences and odd-A +ve parity only show rotational behaviour after ( h 11/2 ) 2 crossing….
Even simpler to just take E (I->!-2) / I for odd-A e.g., R = [ E (15/2 - ->11/2 - ) / (11/2) ]
Summary and Future Look 101,102 Ru (and neighbours) look like -soft, anharmonic vib. nuclei at low-spins (eg. E(4 + )/E(2 + )~2.3)..... BUT also have apparent rotational-like behaviour eg. band-crossing, alignments etc. Paradoxically, Coriolis (rotational) effects are largest in nuclei which have SMALL deformations (ie. require large energies/frequencies to rotate). ‘Vibrational’ A=100 may be the best tests of nuclear Coriolis effects. Vibrational – Rotational ‘phase’ change around spin 10? Smooth evolution with crossing of anharmonic vibrational states and rotation-aligned configurations. ‘E-GOS’ Plot of E /J vs. J gives model independent information on vibrational-rotational crossing. Lifetime (RDM) measurements needed for further work.
many thanks to...... Arata Yamamoto, Scott Langdown (Surrey/Yale students). 101-102 Ru Expt. Con Beausang (+ other Yalies, Des, Gulhan, Mark, Jo… ) 100 Mo+ 136 Xe CHICO, Rochester (Chin-Yen Wu, Doug Cline et al.,), Manc. (John Smith et al,) + LBNL (Augusto Macchiavelli, Paul Fallon et al.,) Vibrator-Rotator (E-GOS) plots, Con B., Rick Casten, Victor Zamfir, Jing-Ye Zhang et al., Odd-A, Carl Wheldon (ex-Surrey now at HMI-Berlin) TRS calcs, Furong Xu (Peking University).
International Conference On NUclear STructure, Astrophysics & Reactions University of Surrey, Guildford, UK 5-8 January 2005 http://www.ph.surrey.ac.uk/cnrp/nustar05
GOOD LUCK CON & CINDY! The south (Munster) has risen again!