fulltext

Even-even-like alpha- and cluster emitters

) National Institute of Physics and Nuclear Engineering - Bucharest, Romania (

2

) Institut f¨ur Theoretische Physik der Universit¨at - Frankfurt am Main, Germany (

3

) Institut de Physique Nucl´eaire - Orsay, France

(ricevuto il 29 Luglio 1997; approvato il 15 Ottobre 1997)

Summary. — The strongest- or cluster transitions in even-even nuclei usually occur

from the ground state (g.s.) of the parent to the g.s. of the daughter nucleus. We perform a systematic search for transitions in nuclei with odd-number of protons and/or neutrons, obeying to the same rules. Universal curves, Geiger-Nuttall plots, and a semiempirical relationship derived from the fission theory of-decay are used.

PACS 23.60 –decay.

PACS 23.70 – Heavy-particle decay. PACS 01.30.Cc – Conference proceedings.

1. – Introduction

New decay modes have been discovered during the last two decades (see [1-4] and the references therein). Cluster radioactivities were predicted [5] in 1980. The first successful experiment was reported [6] four years later.

A large wealth of experimental data on -decay (see fig. 1) and cluster ( 14 C, 20 O, 23 F, 24,26 Ne, 28;30 Mg, and 32;34

Si) radioactivities is available at present [7-11]. Alpha emission [12] is the main decay mode of the heaviest elements [13, 14].

Very frequently, the measured quantities: half-lives,T j

=T 

=i

j, and released

ener-gies,Q

j, of transitions towards the ground state (g.s.) and excited states of the daughter

with intensitiesi

jrelative to the total

strength(j=1;2;:::n; P n 1 i j =1)are available

for a given parent nucleus. As a rule, the strongest transitions in even-even (ee) nuclei occur from the g.s. to g.s. The partial half-life (T

1) systematics of ee nuclides is relatively

smooth, and the accuracy of a semiempirical formula [12] is much higher than for nuclei with odd number of neutrons or/and protons, for which the nuclear structure effects are extremely important.

( 

)Paper presented at the 174. WE-Heraeus-Seminar “New Ideas on Clustering in Nuclear and

Atomic Physics”, Rauischholzhausen (Germany), 9-13 June 1997.

A transition can be favoured or hindered if the wave function of the daughter is very similar or very different from that of the parent, respectively (the overlap integral is large or small). A transition from the g.s. of the parent to an excited state of the daughter can be stronger than one from g.s. to g.s. This fine structure of-decay has been observed

for the first time in 1929 by Rosenblum in Orsay. For a nucleus not measured until now, it is difficult to estimate theQ-value of the strongest transition, because we do not know a priori which transition is favoured. Consequently, generally speaking, the predicted

half-lives of odd-mass or odd-odd nuclei are not as reliable as those of the ee ones. The purpose of the present work is to search for odd-mass or odd-odd nuclei obeying to the rules valid for ee ones.

Fig. 1. – Regions of alpha emitters relative to the Green approximation for the line of-stability. NandZare the neutron and proton numbers.

Cluster transitions with excited fragments (daughter nucleus or emitted cluster) have been discussed for the first time by Martin Greiner and Werner Scheid [15] in 1986. The fine structure of the14

C decay of233

Ra has been discovered [16] in 1989 with the super-conducting spectrometer SOLENO in Orsay. This unique instrument has been used again in 1995 to perform [17] the most accurate experiment on the14

2. – Preformation and penetrability

The quantum tunneling through a potential barrier (e.g. E(R )) is the main

physi-cal phenomenon explaining some nuclear disintegration processes. We had developed numerical- (NuSAF) and analytical superasymmetric fission (ASAF) models, allowing to describe in a unified manner three groups of decay modes:-decay, cluster emission, and

cold fission.

The basic relationship employed both in alpha-like or fission-like theories [1] allows us to express a measurable decay constant,  = ln2=T as a product of three

model-dependent quantities:

=SP;

(1)

where is the frequency of assaults on the barrier,S is the preformation probability of

the cluster at the nuclear surface, andP (orP

sin fig. 3) is the quantum penetrability of

the external part of the barrier from the touching point configuration, where the distance between the fragment centers is R

t = R

d +R

e, up to the external turning point R

b,

defined byE(R b

)=Q.

Fig. 2. – The quantitiesF =(ln2)=,S,Pwithin NuSAF model and the calculated and measured

half-lifeTvs. the mass number of emitter nucleus for some cluster decay modes (C, O, Ne, Mg, and

Si isotopes).

According to our method, developed in 1990, the preformation probability in a fission model [1] can be calculated within the quasiclassical WKB approximation, as the penetra-bility of the internal part of the barrier:

S=exp[,K ov ] K ov = 2  h Z Rt Ra p 2B(R )[E(R ),Q]dR (2)

in whichB(R )is the nuclear inertia andR

athe internal turning point, defined by E(R a )= Q. The WKB equations P =exp[,K s ]; K s = 2  h Z Rb Rt p 2B(R )[E(R ),Q]dR ; (3) whereR

bis the external turning point ( E(R

b

) =Q), are generally used to calculate the

penetrability of the external part of the barrier.

The fact that not every quantity from eq. (1) plays an equally important role is illus-trated in fig. 2, where the penetrabilty dominates the half-life variation withA. One can

see how within the NuSAF model the factorF = (ln2)= (dot-dashed curve) remains

practically constant, the preformation (dashed curve) differs from one decay mode to an-other but it is not changed very much for a given radioactivity, while the general trend of penetrability (dotted curve) follows closely that of the half-life (full curve). It means that for cluster radioactivity and-decay as well, the external part of the barrier, essentially

of Coulomb nature, is much wider than the internal part. Consequently, both fission-like and-like models, which take into consideration the external part of the barrier in the

same manner, can provide a successful explanation for the measured half-lives. In a first approximation one can consider=const, and

S=S

(Ae,1)=3 

:

(4)

From a fit of experimental data we got:S

= 0.0160694 and  = 10 22:01 s,1 . Any depen-dence onZ e ;Z

dand the neutron number N

dhas been neglected. For cluster emission this

choice is justified from a practical point of view, in what concerns the daughter nucleus. We have shown, indeed, on the basis of a large amount of systematic calculations within the ASAF model, that in the most interesting region of parent nuclei, the heavy fragment is almost always the doubly magic nucleus208

Pb or one of its neighbours.

Based on these observation, a universal curve for each kind of cluster decay mode has been obtained: logT =,logP s ,22:169+0:598(A e ,1): (5)

This equation represents a straight line for a givenA

ewith a slope equal to unity (see fig.

3). The vertical distance between two universal curves corresponding toA e1and A e2is 0:598(A e2 ,A e1

). For any combination of fragmentsA e Z e, A d Z

done can calculate easily

,logP s =0:22873( A Z d Z e R b ) 1=2 [arccos p r, p r(1,r) ]; (6) wherer=R t =R b, R t =1:2249(A 1=3 d +A 1=3 e ),R b =1:43998Z d Z e =Q, and A =A d A e =Ais

the reduced mass number.

Instead of having different lines for variousZ of parent nuclei, like in the

systemat-icslogT =f(Q ,1=2

), one gets practically only one line when we plotlogT = f(logP s

).

One can see (fig. 3) how nicely the experimental points for-decay and 14

C radioactiv-ity of even-even nuclei are lying on the corresponding universal curve, compared to the traditional “Geiger-Nuttall” plot for which the points are very scattered.

3. – Even-even-like emitters

On the left-hand side of fig. 3 we considered two 14

C transitions from 223

Ra. The favoured one, going to the first excited state of209

Pb, behaves like a g.s.!g.s.

transi-tion in even-even nuclei, both on the universal curve and on the Geiger-Nuttall plot. The hindered transition, toward the g.s. of209

Pb, is very clearly above the two lines.

Fig. 3. – Universal curves (top) and “Geiger-Nuttall” plots (bottom) for14

C radioactivity (left-hand side) and-decay (right-hand side). The alpha emitters are even-even nuclei.

On the other hand one can accept that221

Fr and225

Ac behave like even-even nuclei (“ee-like14

C emitters”). From a similar plot for24

Ne decay, one can say that231

Pa and235

U are ee-like24

Ne emitters, but the g.s.!g.s.

24

Ne transition from233

U is hindered.

TABLEI. – RMS oflog 10

T(s)data for-decay, calculated with a semiempirical formula

special-ized for a given odd-even parity and for the even-even-like nuclei.

Parity ofZandN even-even eoo eoe oeo oee ooo ooe

No. of nuclides 151 51 59 61 42 48 32

RMS (with parity) 0.182 0.243 0.479 0.216 0.300 0.292 1.421 RMS (e-e-like) 0.182 0.687 0.191 0.513 0.202 1.001 0.290

The results of a systematic search for ee-like-emitters are shown in table I, where RMS= (" n X 1 (logT i ,logT exp i ) # =(n,1) ) 1=2 ; (7) in whichT i(

i =1;2;:::n) are calculated by using our semiempirical formula for-decay

[12] with the same parameter values as for ee nuclei in the following groups: ee, eoe, oee, ooe of 151, 59, 42, and 32 even-even, even-odd, odd-even, and odd-odd parity, respectively. As can be seen from table I, for the remaining groups eoo, oeo, and ooo of 51, 61, and 48 even-odd, odd-even and odd-odd nuclei, respectively, better results are obtained when the parameter values of the semiempirical formula in each group are different from those of ee one. We intend to publish elsewhere more details about these groups of nuclides.

REFERENCES

[1] POENARUD. N. and GREINERW., in Nuclear Decay Modes (Institute of Physics Publishing, Bristol) 1996, p. 275.

[2] GREINERW. et al., in Treatise on Heavy Ion Physics , edited by A. BROMLEY, Vol. 8 (Plenum Press, New York) 1989, p. 641.

[3] POENARUD. N. and GREINERW., in Handbook of Nuclear Properties (Oxford University Press, Oxford) 1996, p. 131.

[4] HOURANY E. et al., in Experimental Techniques in Nuclear Physics, edited by D. N. POENARUand W. GREINER(Walter de Gruyter, Berlin) 1997, p.117.

[5] SANDULESCUA., POENARUD. N. and GREINERW., Sov. J. Part. Nucl., 11 (1980) 528. [6] ROSEH. J. and JONESG. A., Nature, 307 (1984) 245.

[7] RYTZA., At. Data Nucl. Data Tables, 47 (1991) 205.

[8] WESTMEIERW. and MERKLINA., (Fachinformationszentrum, Karlsruhe) 29–1 Preprint, 1985.

[9] BUCKB., MERCHANTA. C. and PEREZS. M., At. Data Nucl. Data Tables, 54 (1993) 53. [10] Chapters in [1] by ROECKLE., HOURANYE., BONETTIR. and GUGLIELMETTIA. and in

[3] by J. K. TULI.

[11] TRETYAKOVAS. P. and MIKHEEVV. L., to be published. [12] POENARUD. N., HOURANYE. and GREINERW., in [1], p. 204. [13] HOFMANNS., M ¨UNZENBERGG. et al., Z. Phys. A, 350 (1995) 277, 281. [14] HOFMANNS., M ¨UNZENBERGG. et al., GSI-Nachrichten, 02 (1995) 4. [15] GREINERM. and SCHEIDW., J. Phys. G, 12 (1986) L229.

[16] BRILLARDL. et al., C. R. Acad. Sci., 309 (1989) 1105. [17] HOURANYE. et al., Phys. Rev. C, 52 (1995) 267.