GOSIA; Past, Present and Future. Douglas Cline

Transcription

1 GOSIA; Past, Present and Future Douglas Cline Tomasz Czosnyka Coulomb excitation Ching-Yen Wu

2 Acknowledgement Tomasz Czosnyka

3 Genesis of GOSIA 1960 s : Multiple Coulomb excitation development: Heavy-ion accelerators High-resolution Ge γ-ray detectors Winther-de Boer semiclassical COULEX code (1965) : Coulomb excitation reorientation measurements of excited state Q 2 + Magnetic spectrometer and p-γ coincidence techniques used Coulomb Excitation Gamma-Ray Yield code (Cline, Lesser) 1971: 1975-: Development of the rotational-invariant technique (Cline, Flaum) High-Z beams available from the SuperHILAC and UNILAC Coulomb excitation of 104 Ru, 110 Pd, 165 Ho, 166 Er, Os, 194 Pt Visitors: Julian Srebrny (1978), Lennart Hasselgren ( ) Ph.D. Students: Ching-Yen Wu ( ), Tomasz Czosnyka ( )

4 1976: Personal Goals 1) Use multiple Coulomb excitation to measure complete set of E2 matrix elements, including signs and magnitudes, for low-lying states in nuclei. 2) Exploit the Rotational Invariants to extract the expectation values of the centroids and widths for the intrinsic frame E2 properties of low-lying states. 3) Employ the intrinsic frame E2 rotational invariants as a powerful probe of collective motion in nuclei.

5 Achievements ) Model-independent manual analysis of 110 Pd using COULEX/CEGRY determined a set of E2 matrix elements that reproduced the data. (L. Hasselgren and D. Cline, Ettore Majorana Int. Sci. Series, Vol 10 (Ed, F. Iachello, Plenum Press) 1980 p59) 2) GOSIA code developed by Czosnyka, Cline, and Wu, ) GOSIA analysis of 110 Pd data completed and confirmed the manual analysis; ) Recoil-distance lifetime measurements confirmed the correctness and accuracy of the GOSIA analysis. 5) Extensive GOSIA model-independent analysis of the Os, 194 Pt Coulomb excitation data achieved the goals of the program; (C.Y. Wu, Ph.D. thesis, Univ. Rochester 1983, C.Y Wu et al, Nucl. Phys. A607, (1996) 214) 1983: Personal goals fully achieved

6 General features of GOSIA Experiment-oriented modular program to support all stages of Coulomb excitation including simulation plus design and data analysis. Perform least-squares fit to 500 matrix elements (E1, E2, E3, E4, M1, M2) coupling 75 states. E5, and E6 couplings included but not fit. Fit to γ-ray yields from 50 independent experiments, plus branching ratios, E2/M1 mixing ratios, lifetimes, and known matrix elements. Fast semi-analytic approximations to the coupled-channel Coulomb excitation are used to achieve the speed necessary for least-squares fitting and error calculations. The Coulomb excitation and subsequent γ-ray de-excitation are treated as separable processes since the collision time is 10 7 times shorter than the decay time.

7 GOSIA assumptions: Excitation 1) Interaction is purely electromagnetic The Coulomb-nuclear interaction is 10-3 effect for heavy ion collisions if the semiclassical distance of closest approach, d [1.25(A T 1/3 + A P 1/3 ) + 5] fm (D. Cline; Nuclear Physics A133 (1969) 445) 2) Semi-classical approximation Require the Sommerfeld parameter For typical heavy-ion Coulomb excitation 50 η 500 Semiclassical calculation differs by < 5% from full quantal calculation at η = 30 3) Classical hyperbolic Rutherford orbit. Use energy-symmetrized orbit. Orbit perturbation due to atomic screening, vacuum polarization, relativistic effects are negligible and partially cancel. Equivalent to distance of closest approach change < 0.2%.

8 1) Interaction is purely electromagnetic 2) Semi-classical approximation 3) Classical Rutherford orbit. GOSIA : Excitation stage 4) Virtual excitation of unobserved states. 1) Low-lying states: explicitly include in the GOSIA level system at least 2 additional states in each band above the states observed 2) Giant E1 resonance: 12% effect corrected by incorporating the dipole polarization term ( Electromagnetic Excitation, Theory of Coulomb Excitation, North Holland; Alder and Winther) 5) Mutual excitation Includes monopole-multipole Coulomb excitation of either the target or projectile Can ignore the small multipole-multipole interaction terms since they do not interfere with the monopole-multipole terms. Calculated to be 0.05% effect for 76 Se on 48 Ti (Kavka). 6) Particle solid angle and target thickness Exact numerical integration over solid angle of particle detectors and target thickness

9 GOSIA: γ-ray decay: 1) Input calculated statistical tensors 2) Cascade feeding Fully included 3) Hyperfine interactions 1) γ-ray angular correlation greatly perturbed by hyperfine interactions between the excited nuclear static moments and the atomic field of the highly-ionized, rapidly- decaying atom. 2) Atomic decay a stochastic process, time and magnitude of atomic fields not calculable 3) Use the Brenn and Spehl two-state model of the deorientation effect which works well. Assume: Fluctuating field as atomic electrons cascade down Static field for equilibrium ionized atomic state Use average parameters taken from analysis of prior data. F. Brenn, H. Spehl et al, Zeit. Physik A281 (1977) 219, A.E. Kavka, Ph.D. thesis ) Future development: Calculable model of atomic fields can be used with GOSIA to measure excited state magnetic moments.

10 2) Cascade feeding 3) Hyperfine interactions 4) Relativistic transformation GOSIA: γ-ray decay: (P.M.S.Lesser, Ph. D. Thesis, Univ. Rochester, 1971) 5) Gamma-ray detector solid angle Assume axial symmetric γ-ray detector with γ-ray emitter on symmetry axis Calculate energy-dependent attenuation factors Q k where k = 1, 2, 3, 4, 5, 6, 7, 8. Future development: Allow any shaped γ-ray detector. Use GEANT to calculate the full detection efficiency tensor ε k,κ. as a function of γ-ray energy. 6) In-flight decay For decay lifetimes in the nanosecond range the emitting nucleus is displaced from the target position by several centimeters changing the emission angle and solid angle subtended by γ-ray detectors. A first-order time-of-flight correction is available in GOSIA.

11 E2 Rotational Invariants

12 E2 Rotational Invariants GOSIA evaluates the invariants for different spin couplings plus the errors Invariants are ideal for studies of shape-transitional nuclei

13 GOSIA variants: PAWEL T. Czosnyka, (Warsaw) 1992 Designed to handle Coulomb excitation of an excited isomeric state. Allows for the case where the target is a mixture of nuclei in either the ground or isomeric states. ANNL R. Ibbotson, (Rochester) 1995 Exploits the principle of simulated annealing to overcome difficulties of trapping in secondary minima by steepest-descent minimization. Introduce a Cauchy-Lorentz noise distribution corresponding to temperature T to sample over the χ 2 distribution. Gradually reduce temperature to locate minima. GOSIA2 T. Czosnyka, (Warsaw) 2005 Simultaneously handle Coulomb excitation of both target and projectile for radioactive beam applications. Ignores the multipole-multipole interaction term.

14 GOSIA Coding Originally based on the 1978 version of the Coulomb excitation code COULEX (Winther, de Boer) plus the γ-ray deexcitation code CEGRY (Cline, Lesser, et al). The coding was rewritten by Czosnyka to achieve speed and efficiency. The similarity of structure and subroutine names with source codes is misleading. Coding is heavily overlaid to minimize memory, [1.5MB] and maximize speed. Complexity and overlaying of code has inhibited modifications of the coding. Only minor evolutionary refinements to the coding during : Czosnyka, Hayes and Cline coordinated upgrades and synchronization of Rochester and Warsaw versions of the codes. This 2006 version is available at

15 GOSIA Coding Major coding upgrade: Nigel Warr 1) Discovered and corrected an error in the rotation matrix subroutine 2) Explicitly specified 64-bit precision to ensure reliable compilation 3) Reordered common blocks with 64-bit variable before 32-bit variables 4) Replaced archaic Fortran77 statements with modern counterparts. 5) Restructured the code to unravel loops and go to statements 6) Indented code to make loops and if statements more obvious 7) Added more robust error recognition and job termination 8) Updated GOSIA2 to match GOSIA This 2007 version of the GOSIA is available at : Remaining deficiencies: 1) Heavily overlaid code is difficult to understand, maintain, and upgrade. 2) Insufficient coupled channels to handle current work. 3) Code requires more intelligence and error checking Restructuring the codes would facilitate use, maintenance, and future upgrades

16 Website: GOSIA Documentation Latest versions of the source codes, (28 March 2008) Sample input files. Latest version of GOSIA User Manual. (3 April 2008) List of updates, release notes. Web Forum being added to facilitate communication. Propose to add an updated GOSIA publication list User Manual: User Manual has been updated and maintained at Rochester. Includes instructions for all of the GOSIA suite of codes Tutorial chapter 11 added by Adam Hayes to assist the new user.

17 Applications of GOSIA (Rochester) 1) Shape-transitional nuclei: 72 Ge, 76,80,82 Se, 104 Ru, 106,108,110 Pd, 114 Cd, 128 Xe 182,184 W, 186,188,190, 192 Os, 194 Pt 2) Strongly-deformed nuclei: 152 Sm, 156 Gd, 162 Dy, 165 Ho, 166,168 Er, 235,238 U, 248 Cm 3) Octupole collectivity: 96 Zr, 148,150 Nd, 150 Sm, 208 Pb 4) Isomeric states: 178 Hf, 242 Am 5) Radioactive beams: 20, 21, 29 Na

18 Two-phonon states in 110 Pd Used 208 Pb, 58 Ni, 16 O beams. Observed p-γ coincidences. a) Manual analysis b) GOSIA c) Measured 8 lifetimes by recoil distance method. Determined 110 E2 and 9 M1 matrix elements. (L. Hasselgren and D. Cline, Ettore Majorana Int. Sci. Ser., Vol 10 (Plenum Press) (1980)59) B. Kotlinski et al; Nucl. Phys. A503(1989)575

19 Hasselgren et al, 1980

20 Two-phonon states in 110 Pd: Conclusions 1) Proved feasibility of model-independent determination of the signs and magnitudes of E2 matrix elements from multiple Coulomb excitation data using GOSIA. 2) Completeness and identities of rotational invariants satisfied 3) The harmonic vibrator model description is incorrect. The appearance of a two-phonon triplet is fortuitous 4) One has strong mixing of coexisting soft vibrational quadrupole-deformed configurations (L. Hasselgren and D. Cline, Ettore Majorana Int. Sci. Ser., Vol 10 (Plenum Press) (1980)59) B. Kotlinski et al; Nucl. Phys. A503(1989)575

21 Shape transition in 186,188,190,192 Os, 194 Pt 40 Ca, 58 Ni, 136 Xe, 208 Pb beams. Observed p-γ coincidences. Observe: gsb, γ, 4 +, 0 + bands 192 Os determined 36 E2 matrix elements. C.Y. Wu et al: Ph.D. Thesis; Rochester 1983; Nuclear Physics A607 (1996) 178

22 Centroid spin dependence C.Y. Wu et al: Ph.D. Thesis; Rochester 1983; Nuclear Physics A607 (1996) 178

23 Mass dependence of ground-state E2 invariants C.Y. Wu et al: Ph.D. Thesis; Rochester 1983; Nuclear Physics A607 (1996) 178

24 Study of 182,184 W, 186,188,190, 192 Os, 194 Pt C.Y. Wu et al: This remarkable piece of work involved an enormous analysis task done in parallel with development of GOSIA. Confirmed the feasibility of model independent analysis of multiple Coulomb excitation data. This work played a key role during the development and testing of GOSIA. This study clearly elucidates the smooth shape transition from prolate strongly-deformed shapes, in the lighter nuclei, to less deformed triaxial shapes that have considerable softness to triaxial vibrations approaching the 208 Pb doubly-closed shell. Ph.D. Thesis; Rochester 1983; Nuclear Physics A533 (1991) 369, Nuclear Physics A607 (1996) 178

25 Recent Coulomb excitation studies Gammasphere plus CHICO: High-spin physics: 238 U, Populated seven bands to I 40 (Simon, Cline, Vetter, Wu et al) High transition density: Complete spectroscopy: Isomeric states: 235 U, Observed 300 resolved transitions (Ward et al, AIP Conf. Proc. 764 (2005)263) 152 Sm, Observe 111 levels below 2.4 MeV (Kulp et al, Phys. Rev. C71 (2005)041303) 178 Hf, Populate 31 year, K = 16 + isomer (Hayes et al, Phy. Rev C75(2007)034308) High target radioactivity: 242m Am, 1.6 millici, γ-rays ~ /sec α-particles ~ 10 6 /sec (Hayes et al, Laser Phys. 17 (2007)745) TIGRESS/Bambino: Radioactive beams: 20, 21 Na (Schumaker et al, Int. Conf. Tokyo, 2007) 29 Na (Hurst et al)

26 Low-energy CoulEx of 29 TRIUMF/ISAC-II Motivation: Competition between normal [sd] and intruder [pf] dominated configurations with increasing N Narrowing of effective sd-pf shell gap 29 Na: a transition-point nucleus to Island of Inversion for Z = 11 isotopic chain? Measure B(E2) value; provides insight into deformation effects Experimental details: 110 Pd( 29 Na, MeV I b ~ pps on Coulex target γ-ray detection: TIGRESS i.e. 6 x 32-fold HPGe clovers with suppression scintillators particle detection: BAMBINO i.e. 24 annular x 32 sector Si strips data collected in August 2007 A. M. Hurst for the TIGRESS collaboration

27 29 Na Coulomb excitation results BAMBINO particle-energy spectrum reveals two-component isobaric beam mixture With energy loss of 70 MeV beam in 110 Pd foil and 197 Au layer on BAMBINO strips: E p ( 29 Na) = 50.2 MeV, E p ( 29 Al) = 45.1 MeV, in agreement with calculated energy loss First evidence for isobaric separation using thin-target CoulEx technique Integrated Rutherford peaks from BAMBINO spectrum allow us to determine beam composition: Beam fraction of 29 Na ~ 72.0(15) % Particle-γ coincidence Clover addback Random subtraction Compton suppressed E γ ( kev, E γ ( kev Relative measurement of γ-ray intensities yields B(E2) value for 29 Na A. M. Hurst for the TIGRESS collaboration

28 Extracted B(E2) value for 29 Na A. M. Hurst for the TIGRESS collaboration Vary M(E2) in GOSIA in order to reproduce experimental yield Negligible sensitivity to reorientation effect Impact on γ-ray angular distribution due to M1-dominated 72-keV transition is also negligible Excitation to higher-lying states in 29 Na expected to be significantly weaker (< 1 %) than the observed 5/2 + 3/2 gs+ transition B(E2) value indicates significant collectivity, 16 WU, develops for N = 18 nucleus 29 Na B(E2) in better agreement with SDPF-M Monte Carlo Shell Model prediction than with the USD model B(E2) value indicative of large degree of mixing (~42 %) from intruder pf orbitals in the wavefunction of the 5/2 + state. Publication in preparation.

29 The Future Nuclear Science: Physics of exotic nuclei far from stability is the new frontier of the field. Coulomb excitation will play a major role in this research program. Radioactive beam facilities: Near term: ANL-CARIBU, GANIL, HRIBF, REX-ISOLDE, TRIUMF-ISAC2 Long term: FAIR, FRIB Orders of magnitude increase in exotic-beam intensities Instrumentation: γ-ray detectors: Gammasphere, Euroball, TIGRESS, MINIBALL, GRETA, AGATA, Heavy-ion detectors: SuperCHICO, Bambino, etc 400-fold improvement in sensitivity for Coulomb excitation

30 Required coding upgrades of GOSIA 1) Simplify coding of GOSIA Eliminate overlaid coding to facilitate current and future development. 2) Simplify GOSIA input and use: (Adam Hayes) Build more decision making and error checking into the code. Automate input of energy-loss, electron conversion coefficients, detection efficiency ε k,κ tensors, etc. 3) More coupled channels: Improved experimental sensitivity will involve more excited states and coupled channels. Now require at least 150 levels and 1500 matrix elements, more in the future. 4) Use full γ-ray detection efficiency tensor: Allow use of non-axially symmetric γ-ray detectors. Use GEANT4 to calculate the full detection efficiency tensor, ε k,κ as a function of γ-ray energy. 5) Model-dependent fitting: (Adam Hayes) Allow flexible user-defined coupling algorithms relating matrix elements

31 Extend GOSIA capability 1) Analysis of p-γ-γ data: (Kasia Wrzosek) p-γ-γ data provide the highest sensitivity data with modern arrays Angular correlation data determines spin and γ-ray multipole mixing ratios. Sum over particle and γ-ray detectors selected according to known angle symmetry properties to optimize the balance between the number of spectra analyzed, the statistical accuracy, and maximum angular correlation sensitivity. 2) Electron spectroscopy: (Emmanuel Clement) Add particle-electron coincidence data to the GOSIA input data set 3) Excited state magnetic moments: Import a calculable theory of atomic hyperfine interactions when available 4) Enhanced simulation: (Jedrzej Iwanicki) Couple GOSIA to GEANT4 for simulation and analyzing experiments

32 GOSIA Development and Management Establish a formal GOSIA User Group to stimulate, set standards, and manage development, maintenance, and quality assurance testing of the GOSIA suite of codes. GOSIA User Group: Membership: Any registered user of GOSIA Goals: Promote, prioritize, facilitate, and coordinate development Manage GOSIA maintenance, standards, plus quality assurance testing GOSIA Users Steering Committee: Membership: An elected representation balanced geographically plus expertise. Purpose: Execute the goals of the User Group Provide reports and recommendations to the User Group Manage a GOSIA website, library of latest codes, and user manual Promote and facilitate use of GOSIA Facilitate communication between users, workshops etc

33 Conclusions GOSIA has played a major role in Coulomb excitation work for 27 years Coulomb excitation will play a prominent role in the future of the field requiring continued development and use of GOSIA. Upgrades to the coding and addition of new capabilities to GOSIA are essential to satisfy current and future use. A GOSIA User Group is desirable to manage the codes, as well as promote, prioritize, facilitate, and coordinate future development.

34 Acknowledgements Tomasz Czosnyka Ching-Yen Wu Lennart Hasselgren Adam Hayes Rich Ibbotson Alexander Kavka Bodan Kotlinski Mike Simon Julian Srebrny Ehrenfried Vogt Anders Backlin Peter Butler Nigel Clarkson Claes Fahlander Aaron Hurst Pawel Napiorkowski Mike Schumaker John F. Smith Lars Erik Svensson Ingvar Thorslund Bjorn Varnestig Nigel Warr Chris White Gosia coding Graduate work

35 Acknowledgement Tomasz Czosnyka