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University of Groningen

Development of an atomic clock for fission lifetime measurementsKravchuk, Vladimir Leonidovich

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Publication date:2004

Link to publication in University of Groningen/UMCG research database

Citation for published version (APA):Kravchuk, V. L. (2004). Development of an atomic clock for fission lifetime measurements. Groningen: s.n.

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Download date: 05-01-2020

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with GBW the Bohr-Wheeler fission width, g the nuclear vis-cosity, t the time, and t the time at which the flux across thebarrier reaches 90% of the quasistationary value. We param-etrized t anew from the results of Grange et al.

t~b ,T !5~2g !21ln~10E f /T !10.0112gA/T @10221 s# . ~4!

Here, E f is the height of the fission barrier, T is the tempera-ture, and A is the mass number. t has been calculated forevery nuclear state in the cascade. Another expression for twas obtained by Bhatt et al. @16#, but the g-ray spectra cal-culated with this expression are hardly different.

In the original version of CASCADE the probability fordecay of a nucleus moving from the saddle point to the sciss-ion point is not calculated. To take this effect into account,the fission width has been treated analogously to the fissionflux. The flux at time t at the saddle point is ~almost! equal to

the flux at the scission point at time t1tssc , with tssc the timerequired to propagate from the saddle point to the scissionpoint @17#:

tssc5tssc0 ~A11g2

1g !. ~5!

From the graphs presented by Grange et al. @15#, a value fortssc0 the saddle-to-scission time in nonviscous nuclei, can beinferred: tssc

052.2310221 s. Assuming the same time depen-

dence for the fission width, one can approximate the latter asfollows:

G f~ t !50, t,tssc

5G fBW~A11g2

2g !

[email protected]~ t1td2tssc!/t#%, t.tssc . ~6!

The concept of time, which is unknown in the statistical codeCASCADE, was implemented as follows. The lifetime td of anuclear state with excitation energy E* and angular momen-tum J , which is used as a time step in the calculations, isgiven by

td5\

Gn~E*,J !1Gp~E*,J !1Ga~E*,J !1Gg~E*,J !1G f~E*,J ,t !~7!

in which Gn etc. are the decay widths for all decay channelstaken into account by CASCADE: i.e., neutron, proton, a par-ticle, g ray, and fission decay. The justification for the use ofG f in this equation is that the lifetime of a state is inverselyproportional to the total width including G f . The bookkeep-ing of these time increments is done in matrices t(E*,J)with the same dimensions as the matrices for the populationcross sections, i.e., every nuclear state is characterized by the

charge, mass, excitation energy, angular momentum, and thetime at which the decay to it took place. Note that Eqs. ~6!and ~7! are coupled; therefore, they are solved iteratively.Including G f in Eq. ~7! will influence through the coupling toEq. ~6! the fission probability and thereby the GDR yield.

In the original CASCADE code no distinction is made be-tween compound nuclear fission and quasifission. We imple-mented this distinction as follows. With the one-body dissi-

FIG. 2. Results of the fits of the GDR parameters at four differ-ent values of g, for the experiment with Eb5216 MeV. The solidcurve indicates the sum of the prefission spectrum ~short-dashedcurve! and the postfission spectrum ~long-dashed curve!. For com-parison, a calculation with g55 is also shown ~dotted curve!.

TABLE I. Results of the fission time scale for the differentvalues for the viscosity.

Eb g Bscale t fa

@MeV# ~10220 s)

216 0.01 1.0 4567216 0.1 1.2 1565216 1 1.0 4768216 4 0.7 49362238 0.01 0.8 4561238 0.1 1.0 861238 1 0.8 4761238 2 0.65 24061

aThe numbers used as error bars indicate the sensitivity to thethreshold on the fission cross sections that is taken into account inthe calculation. Here, it represents the difference in t f for thresholdof s f50.5 mb compared to 0 threshold.

54 R1517VISCOSITY AND FISSION TIME SCALE OF 156Dy

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