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EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture V

EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture V. Ranjan Bhowmik Inter University Accelerator Centre New Delhi -110067. MEASUREMNENT OF NUCLEAR LIFETIMES. NUCLEAR LIFE TIME.

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EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture V

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

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

  3. NUCLEAR LIFE TIME • The transition probability for g-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 Eg and multipolarity  . Lecture V SERC-6 School March 13-April 2,2006

  4. Weisskopf Single Particle Estimate 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. ELECTRIC MAGNETIC Lecture V SERC-6 School March 13-April 2,2006

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

  6. Nuclear Quadrupole Deformation • For deformed nuclei, the deformation b is related to the intrinsic Quadrupole moment Q0 Q0 is related to B(E2) for collective E2 transitions Lifetime is related to Q0 by the expression: 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) = N0 exp(- t / t) for mean life time t • t = 1/l where l is the total transition probability • If t > ns, it can be measured by direct timing with a Ge detector using the following techniques : • Irradiation & counting ( > min) • Tagged spectroscopy ( > ms) • Pulsed beam technique ( ns - ms) • g-g 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) 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 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 & g-decay measured with TAC • Suitable for life-times ms -ms range PRC 70(2004) 014311 Transport Time ~ ms Lecture V SERC-6 School March 13-April 2,2006

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

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

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

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

  14. g- g Coincidence • For DC beam, g-g 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 Lecture V SERC-6 School March 13-April 2,2006

  15. Multi coincidence method • Poor time resolution of Ge limitation t > ~ns isomers • Excellent energy resolution compared to scintillators • Fast scintillators available for timing with g or b particles ( Dt < 500 ps) Fast plastic for detection of b BaF2 for g-detection ( Dt ~ 300 ps) • Ge with good energy resolution used for channel selection, other two for g-g or b-g timing • Applicable for g-g-g or b-g-g coincidences with Ge-BaF2-BaF2 or plastic-Ge-BaF2 NIM280(1989)49 Lecture V SERC-6 School March 13-April 2,2006

  16. g- g - g Coincidence J.of.Phys.G31 (2005)S1421 • Lifetime of 627 keV level of 48V : T1/2 ~ 77 ps Ge-BaF2-BaF2 coincidence allows channel selection by Ge and timing by BaF2 Can we do pulsed beam-g-g coincidence ? 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 1mm in 3 ps • Can be used to provide a time scale ~ ps in terms of distance of travel • Distinguish g-emission from stopped or in-flight recoils by the Doppler energy shift of g-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) Lecture V SERC-6 School March 13-April 2,2006

  18. Recoil Distance Doppler Shift ( RDDS or RDM) • Thin target ~ 500 mg/cm2 • Recoils decay in flight • Stopped by a thick foil known as Plunger • g-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 Lecture V SERC-6 School March 13-April 2,2006

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

  20. Recoil Distance Plunger Setup • Thin target ( ~ 500 mg/cm2) stretched wrinkle-free • Stopper (Au) stretched foil parallel to target • Linear motor for changing target-stopper distance Lecture V SERC-6 School March 13-April 2,2006

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

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

  23. RDM Decay Curve • Distance measured to 0.1 mby 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 Lecture V SERC-6 School March 13-April 2,2006

  24. Multi-level decay • Three level decay where I3 decays exponentially to I2 and I2 has a life time t2 • N3(t) = N0 exp(-t/t3) • dN2/dt = dN3/dt - N2/t2 • growth feeding decay • N3(t) = a expt(-t/t2) + b exp(-t/t3) • "Effective decay time" would depend on both t2 & t3 • Decay curves for preceding transitions have to be measured t3= 50 ps t2 varied t2 = 50 ps t3 = 0-150 ps T.K. Alexander and J.S. Forster, Adv. Nucl. Phys. 10 (1979) 197. 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 ti of the level and the apparent lifetime is given by Bateman Equation : In acascade 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: Lecture V SERC-6 School March 13-April 2,2006

  26. Data Analysis for RDM • LIFETIME program J.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 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 Iu for different stopper distances Z. Physik. 334(1989)163 • Since all intensities are directly measured lifetime can be extracted • Most sensitive to data for 0.5t < t < 2t • Main uncertainty from unobserved transitions 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 g-array allow coincidence measurements in coincidence with other transitions in cascade • Considerable clean up of spectrum in g-g 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 Ius is not possible B A Z. Physik. 334(1989)163 Lecture V SERC-6 School March 13-April 2,2006

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

  31. DDCM with Gating from TOP EPJA26(2005)153 • Gating by the shifted component from top : 36 independent of feeding lifetime GASP Array 40Ca(40Ca,a2p)74Kr Large Doppler Shift 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 dIss/dx to be measured directly Isu Iss 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 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 qR(t) as a function of time • HISTAVER • From the velocity history, calculate the Doppler shift observed at angle qg as a function of time • LINESHAPE • Calculate thepopulation Ni(t) of the state by solving Bateman equations. • Simulate the energy spectrum in a g-detector from the time dependence of Ni(t) • Compare with actual shape and iterate for minimum 2 Lecture V SERC-6 School March 13-April 2,2006

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

  37. Energy Correlated DSAM • In g - g - time correlation, the second gamma is emitted with probability exp(-Dt/tB) • tB = lifetime of B • Putting narrow gate on T1 measures tB directly • Time spectra for g1 with narrow gate on T2 sensitive to lifetime tA • Insensitive to feeding of tA Lecture V SERC-6 School March 13-April 2,2006

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

  40. Fractional Doppler Shift • SD bands have very large Qt with lifetime < 100 fs • g-emission before significant slowing down of the recoils • Large Doppler shift with angle • Fractional Doppler Shift F(t) = <b>/b0 Lecture V SERC-6 School March 13-April 2,2006

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

  42. Fractional Doppler Shift Q0~ 8 eb Lecture V SERC-6 School March 13-April 2,2006

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

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