1. EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture V Ranjan Bhowmik Inter University Accelerator Centre New Delhi -110067

2. Lecture V SERC-6 School March 13-April 2,2006 2 MEASUREMNENT OF NUCLEAR LIFETIMES

3. Lecture V SERC-6 School March 13-April 2,2006 3 NUCLEAR LIFE TIME The transition probability for  -decay is related to the overlap between initial and final state wave functions: B is the reduced transition probability related to the nuclear matrix elements. Measuring the lifetime gives the information about nuclear matrix elements B(R ) The life time is also dependent on photon energy E  and multipolarity.

4. Lecture V SERC-6 School March 13-April 2,2006 4 Weisskopf Single Particle Estimate ELECTRIC MAGNETIC A crude estimate of the Matrix elements has been given by V.F. Weisskopf assuming single particle wave functions for the nucleons. Matrix elements are usually presented in Weisskopf units to indicate whether they are single particle or collective in nature.

5. Lecture V SERC-6 School March 13-April 2,2006 5 Weisskopf Estimate T in seconds E  in keV A in Atomic Mass Unit

6. Lecture V SERC-6 School March 13-April 2,2006 6 Nuclear Quadrupole Deformation For deformed nuclei, the deformation  is related to the intrinsic Quadrupole moment Q 0 Q 0 is related to B(E2) for collective E2 transitions Lifetime is related to Q 0 by the expression:

7. Lecture V SERC-6 School March 13-April 2,2006 7 Measurement of nuclear life times A collection of nuclei produced at t=0 would decay according to the law :N(t) = N 0 exp(- t /  ) for mean life time   where  is the total transition probability If  > ns, it can be measured by direct timing with a Ge detector using the following techniques : Irradiation & counting ( > min) Tagged spectroscopy ( >  s) Pulsed beam technique ( ns - ms)  coincidence ( ns - 100 ns) For shorter lifetimes, an indirect method has to be used: RDM( ps - ns) DSAM ( 100 fs - ps)FDS ( 10-100 fs)

8. Lecture V SERC-6 School March 13-April 2,2006 8 Irradiation & Counting Life times > 1 min Sample is irradiated to produce the isomer Taken to low-background area Counted using a Ge-detector Life times ~ sec - min Fast transport system: Rabbit or Gas-jet-recoil-transport Repeated irradiations to increase statistics PRC37(1988)2894

9. Lecture V SERC-6 School March 13-April 2,2006 9 Recoil Tagged Spectroscopy In Recoil Tagged Spectroscopy, recoil products transported to low-background area using recoil separator Time difference between arrival of recoil &  -decay measured with TAC Suitable for life-times  s -ms range PRC 70 (2004) 014311 Transport Time ~  s

10. Lecture V SERC-6 School March 13-April 2,2006 10 Pulsed beam Spectroscopy Beam is bunched or chopped to a width <  Repetition rate 100 ns -  s or longer Out of beam  - spectra recorded Exponential decay during "beam off period"

11. Lecture V SERC-6 School March 13-April 2,2006 11 Pulsed Beam Technique PRC55(1997)620 E  = 221 & 384 keV 6  s Isomer CHOPPED BEAM 2  s ON 100  s OFF

12. Lecture V SERC-6 School March 13-April 2,2006 12 Pulsed Beam Technique PRC55(1997)620 BEAM OFF Period  coincidence 384 keV gate

13. Lecture V SERC-6 School March 13-April 2,2006 13 Short Half Lives Exponential decay folded by detector resolution Centroid shift Method For short decay time, compare centroid for delayed  with centroid for prompt  of similar energy PRC65(2002)027301 Shift in centroid is equal to the mean life  of the level

14. Lecture V SERC-6 School March 13-April 2,2006 14  Coincidence  For DC beam,  coincidence technique can be used for locating isomers  Gates on transitions above & below the isomer  Does not depend on the side-feeding from other isomers NPA601(1996)195

15. Lecture V SERC-6 School March 13-April 2,2006 15 Multi coincidence method  Poor time resolution of Ge limitation  > ~ns isomers  Excellent energy resolution compared to scintillators  Fast scintillators available for timing with  or  particles (  t < 500 ps) Fast plastic for detection of  BaF 2 for  -detection (  t ~ 300 ps)  Ge with good energy resolution used for channel selection, other two for  or  timing  Applicable for  or  coincidences with Ge-BaF 2 -BaF 2 or plastic-Ge-BaF 2 NIM280(1989)49

16. Lecture V SERC-6 School March 13-April 2,2006 16  Coincidence Lifetime of 627 keV level of 48 V : T 1/2 ~ 77 ps J.of.Phys.G31 (2005)S1421 Ge-BaF 2 -BaF 2 coincidence allows channel selection by Ge and timing by BaF 2 Can we do pulsed beam-  coincidence ?

17. Lecture V SERC-6 School March 13-April 2,2006 17 LIFETIME MEASUREMENT BY INDIRECT METHODS Nuclei produced in heavy ion induced fusion have large recoil velocities ~ 0.01 -0.02c For v/c = 0.01 recoils travel 1  m in 3 ps Can be used to provide a time scale ~ ps in terms of distance of travel Distinguish  -emission from stopped or in-flight recoils by the Doppler energy shift of  -rays emitted in flight Lifetime measurement using Doppler shift : Recoil Distance Doppler Shift (RDDS) ( 1 ps - 1 ns ) Doppler Shift Attenuation Method ( 100 fs - 1 ps) Fraction Doppler Shift ( 5 - 50 fs)

18. Lecture V SERC-6 School March 13-April 2,2006 18 Recoil Distance Doppler Shift ( RDDS or RDM) Thin target ~ 500  g/cm 2 Recoils decay in flight Stopped by a thick foil known as Plunger  -rays detected both from in-flight and those stopped in Plunger Difference in intensity of two components measured as a function of target-stopper distance

19. Lecture V SERC-6 School March 13-April 2,2006 19 RDM Technique  Doppler shift for detector at   Intensity of in-flight component  Intensity of stopped component  Ratio of the two

20. Lecture V SERC-6 School March 13-April 2,2006 20 Recoil Distance Plunger Setup Thin target ( ~ 500  g/cm 2 ) stretched wrinkle-free Stopper (Au) stretched foil parallel to target Linear motor for changing target-stopper distance

21. Lecture V SERC-6 School March 13-April 2,2006 21

22. Lecture V SERC-6 School March 13-April 2,2006 22  -Spectrum from RDM PRC66(2002)064318

23. Lecture V SERC-6 School March 13-April 2,2006 23 RDM Decay Curve Distance measured to  0.1  by computer control Absolute target-stopper distance calibrated by capacitance measurement Distance scale converted to time scale from average recoil velocity Multiple exponential decay components Feeding from states above with comparable life times

24. Lecture V SERC-6 School March 13-April 2,2006 24 Multi-level decay  3 = 50 ps  2 varied T.K. Alexander and J.S. Forster, Adv. Nucl. Phys. 10 (1979) 197. Three level decay where I 3 decays exponentially to I 2 and I 2 has a life time  2 N 3 (t) = N 0 exp(-t/  3 ) dN 2 /dt = dN 3 /dt - N 2 /  2 growth feeding decay N 3 (t) =  expt(-t/  2 ) +  exp(-t/  3 ) "Effective decay time" would depend on both  2 &  3 Decay curves for preceding transitions have to be measured  2 = 50 ps  3 = 0-150 ps

25. Lecture V SERC-6 School March 13-April 2,2006 25 Bateman Equation For a level being fed from multiple levels, the relation between the intrinsic lifetime  i of the level and the apparent lifetime is given by Bateman Equation : In a cascade of transitions the decay of topmost transition is fitted by an exponential and the time evolution of subsequent levels calculated. Intensities of the un-shifted and shifted peak:

26. Lecture V SERC-6 School March 13-April 2,2006 26 Data Analysis for RDM LIFETIME LIFETIME programJ.C. Wells, ORNL1985 Input : Shifted & un-shifted peak intensities for the cascade Trial values of lifetimes Trial value of Side-feeding lifetime Global search for least square minimization Output: Lifetimes of the states in the cascade Main uncertainty due to insufficient knowledge of side-feeding

27. Lecture V SERC-6 School March 13-April 2,2006 27 Differential Decay Curve Method (DDCM) The Bateman equations can be reformulated in terms of the observed un-shifted intensity I u for different stopper distances Z. Physik. 334(1989)163 Since all intensities are directly measured lifetime can be extracted Most sensitive to data for 0.5  < t < 2  Main uncertainty from unobserved transitions

28. Lecture V SERC-6 School March 13-April 2,2006 28 COINCIDENT DDCM Peak to background in Plunger experiments can be improved by gating with an auxiliary detector. Neutron array gating for proton-rich nuclei Large  -array allow coincidence measurements in coincidence with other transitions in cascade Considerable clean up of spectrum in  coincidence Gating from below equivalent to normal RDM Gating from above completely removes side-feeding Three components in B-A coincidence Due to time ordering of transitions I us is not possible B A Z. Physik. 334(1989)163

29. Lecture V SERC-6 School March 13-April 2,2006 29 COINCIDENT DDCM Probability of detecting both B & A : I BA =   N B (t') exp[- A (t" – t')] dt' dt" with the conditions t', t" >T ; both unshiftedt',t" <T ; both shifted t' T shifted  unshifted B A TargetPlungerB decays A decays t't' t" T 0 TIME

30. Lecture V SERC-6 School March 13-April 2,2006 30 COINCIDENT DDCM There are four variations of this technique : Gating from Top ( A to be measured) Total Gate (s+u): removes background & side-feeding Narrow Gate (s) : direct lifetime measurement Gating from Bottom (B to be measured) Total Gate (s+u) : reduces background Narrow Gate (u) : reduced sensitivity to feeding of B For the second case ( Gate on the Shifted peak of top transition) lifetime of A can be measured directly from the observed coincident intensities without solving Bateman equations.

31. Lecture V SERC-6 School March 13-April 2,2006 31 DDCM with Gating from TOP Gating by the shifted component from top : 36  EPJA26(2005)153 independent of feeding lifetime GASP Array 40 Ca( 40 Ca,  2p) 74 Kr Large Doppler Shift

32. Lecture V SERC-6 School March 13-April 2,2006 32 DDCM with gating from TOP Consistent value of lifetime obtained over the region of sensitivity Other Variations: Thin stopper followed by recoil detector for gating Thin stopper foil to slow down recoils followed by a thick one to stop Allows dI ss /dx to be measured directly I su I ss

33. Lecture V SERC-6 School March 13-April 2,2006 33 Doppler Shift Attenuation Method (DSAM) Thin target backed by high Z stopper material to stop recoils in ~ ps time scale Line-shape profile depends on nuclear lifetime Short life time: full shift Long life time : No shift

34. Lecture V SERC-6 School March 13-April 2,2006 34 LINESHAPE PROGRAM DECHIST Simulate the slowing down history of the recoils in backing; Get v(t) and  R (t) as a function of time HISTAVER From the velocity history, calculate the Doppler shift observed at angle   as a function of time LINESHAPE Calculate the population N i (t) of the state by solving Bateman equations. Simulate the energy spectrum in a  -detector from the time dependence of N i (t) Compare with actual shape and iterate for minimum  2

35. Lecture V SERC-6 School March 13-April 2,2006 35 DSAM Lineshape for 58 Cu PRC63(2000)021301

36. Lecture V SERC-6 School March 13-April 2,2006 36 Side feeding Model  Side feeding lifetimes comparable to cascade life times  Simulated by a Rotational cascade side feeding model  Side-feeding lifetime decreases as we go up in energy

37. Lecture V SERC-6 School March 13-April 2,2006 37 Energy Correlated DSAM In  time  correlation, the second gamma is emitted with probability exp(-  t/      = lifetime of B Putting narrow gate on T1 measures   directly Time spectra for  1 with narrow gate on T2 sensitive to lifetime  A Insensitive to feeding of  A

38. Lecture V SERC-6 School March 13-April 2,2006 38 Narrow Gate on Top (NGT) Side-feeding & top- feeding effects eliminated NIMA437(1999)274

39. Lecture V SERC-6 School March 13-April 2,2006 39 Narrow gate Below (NGB) Shifted component reduced in intensity Change in shape of the DSAM spectrum with narrow gate below used to extract lifetime NIMA417 (1998)150

40. Lecture V SERC-6 School March 13-April 2,2006 40 Fractional Doppler Shift SD bands have very large Q t with lifetime < 100 fs  -emission before significant slowing down of the recoils Large Doppler shift with angle Fractional Doppler Shift F(  ) = /  0

41. Lecture V SERC-6 School March 13-April 2,2006 41 Fractional Doppler Shift PRL76 (1996) 3510  Top of band show full velocity F(  ) ~1  Middle of the band has F(  ) ~ 90% Slower transitions in the bottom of the band have F(  ) < 80% Extract average Quadrupole moment of the band by comparing with simulation

42. Lecture V SERC-6 School March 13-April 2,2006 42 Fractional Doppler Shift Q 0 ~ 8 eb

43. Lecture V SERC-6 School March 13-April 2,2006 43