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Home , Spontaneous fission

CENTRAL INSTITUTE OF PHYSICS INSTITUTE FOR PHYSICS AND NUCLEAR ENGINEERING Bucharest, P.O.Box MG-6, ROMANIA BUCHAREST UNIVERSITY, FACULTY OF PHYSICS Bucharest, P.O.Box MG-6, ROMANIA

^\tf ~ FT-350-*fta9 March Plonic radioactivity versus spontaneous fission in decay of superheavy nuclei

D.B.ION*. R.ION-MIHAI**

M. IVASCU*

\* ^^

Ab4.f./iac-t» In this paper ,th3 pionic radioactivity as dominant decay mode of superheavy elements (SHE) is investigated. The dynamical thresholds as well as the competition between the ground state pionic radioactivity and the spontaneous fission are discussed. It is shown that the usual around the double magic nucleus 29 8[114 ] is destroied via a deep instability due to the spontaneous -,ion emission. An is­ land of relative stability against the pionic dominant decay mode is predicted to be around the magic nucleus [120],The pionic radioactivity dominance in the SHE region can be con­ sidered as one of the possible reasons why SHE nuclei have not been synthesized and/or identified using heavy ion reac­ tions. 1. INTRODUCTION

In some recent papers [1-13J we have initiated the investi­ gation of the spontaneous pion emission from the ground state of a nucleus as a new possible natural radioactivity called pionic nuclear radioactivity. Then, the Q^ - systematics, the definitions of the "width" (T^) and the Lorentz invariant statistical factors of the pionic nuc>ear radioactivity are presented [1-3]. It was shown that this new type of nuclear radioactivity is energetically possible via two (or many)-body fragmentation of the parent nucleus and that the most statistically favoured pionic emitters are those with Z > 92. Experimental detection of the neutral and charqed pions as well as some possible two step mechanisms for the spon­ taneous pion emission are also discussed in ref. [1-6]. An Optical

Theorem for the inclusive pionic radioactivity was- proved [6]. Ex­ tensions of these results to other possible natural radioactivi­ ties, such as muonic nuclear radioactivity, lantbdonic (\°) nuclear radioactivity, hyperfission, etc., are also presented in refs. [2,

7, 13]. The dynamical predictions for the pionic nuclear radioac­ tivity were obtained in refs. [ 8-12 ]. The credibility of these predictions is verified by applying the same fission-like model

[ see e.g. refs. [ 11-13 ]] to the light-charged-particle (LCP) emis­ sion data. Moreover, the absolute predictions for the yieldr /rs are in agreement with the experimental upper limits obtained at

Bucharest [14-16] for charged pions and also with those measured at: CEN - Saclay [17], ORNL [18], and TRIUMF-Vancouver [19]for neutral pions. Also, it is important to note that, recently [21], the unusual background observed experimentally by Wild et al El ] in the (AE, E) - region below that characteristic of LRA's - 2 -

257 emission from Fm is interpreted by us as being produced by 257 negative pions emitted spontaneously by Fm. If this interpreta­ tion is correct then the inferred value of the negative pionic 257 -3 yield of Fm is r /rCc = 1° • This result is with ten orders II or of magnitude higher than that predicted by us in ref. [10].

Now, we remember that in refs. [5,12] we pointed ^ut that: the discovery of the pionic radioactivity will contribute to a much deeper understanding of the nuclear instabilities in the region of the superheavy elements where the ground state jnowic ra­ dioactivity is expected to be one of the dominant nuclear decay m ode. Consequently a detailed investigation of this last conjec­ ture is needed. So, in this paper, the fission-like model [ 12] is applied for the calculation of the pionic yields (^-„/^cc) for the superheavy elements in terms of their spontaneous fission half-lives. The Q -systematic for the superheavy elements (SHE) is presented in Section 2, wm'le the dynamical thresholds for the ground state pionic radioactivity are discussed in Section 3. The competition between tK« pionic radioactivity ind spontaneous fission in decay of the ' is investigated in

Section 4 while the conclusions are sutmarized in Section 5.

2. Q - SYSTEMATICS FOR SUPERHEAVY ELEMENTS IT

Superheavy elements (SHE) have been postulated in 1955 by

Wheeler [22] and in 1967 by Scharf Goldhaber [231. But the inter­ national interest in detection and synthesizatlon of these elements began in the latter part of 1960's as a result of the theoretical predictions [23] for their localization around the doubly magic nucleus 292[H4]. So predictions given by Myers and Swiateckl [24],

Strutlnsky [25], Meldner *.26], Nilsson [27], N1x [28] and their - 3 - co-workers, have given the naif-lives we can expect for the nuclei from the island of stability arcund element 114. They rar.qe in 9 294 this island as high as 10 years e.g. for 110 . Another .-.land of stability has been predicted 1291 to exist around element

V21164 1. The continuing progress "n synthesis and study of the pro­ perties of the heaviest nuclei 130-33: demands further improvements in the theoretical predictions of these r;UCiiJes. Various methods of calculations of the ground state o.t:-rqy and fission barriers and various models for description of the internal structure of these nuclei have been used, leading to many different estimates of their lifetime [see e.g. reviews |36-39)| . Most searches for

SHE's in nature and at heavy ion accelerators have used spontaneous fission as detection methods Isee e .q . ref. [35]] . This is because of extreme sensitivity ana iow b-trkground offered by this method and the expectation that superheavy nuclei will either decay by spontaneous fission themselves or at least r!<-cay by another nuclide which will decay by spontaneous fission. 1,'nfor tunatel y to date no

superheavy elements have been discovered. Several possible reasons why SHE's have not been synthesized and/or identified using heavy

ion reactioni are analysed in ref. 140].

Here, we analyse in more detail the possibility of the competition between the spontaneous pion emission and the sponta­

neous fission in the decay of superheavy elements suggested in refs. [5,12], As we can see in Section 4, this new hypothesis can explain why the efforts to synthesize and identify superheavy elements using heavy-.on reactions have been unsuccessful up to present time. - 4 -

The ground state pion radioactivity is energetically pos­

sible only accompanied by the spontaneous fission of the parent

nucleus. Hence, we start our discussion with the following :

(A,Z) > •: • (Aj. Zj) + (A2, Z2) (2.1a)

with

A = AL + A2, Z = Z^ + Z, + Z2 (2.1b)

where A, A,, A- and Z, Z., Z2 are the usual mass numbers and charge numbers of the involved nuclei, while Z« denotes the pion charge. If the nuclear masses: H(A,Z) - M, M(A.,Z.) = n., i = 1,2, and also the pion rest mass m , are given in units of energy, then

the total energy liberated in the reaction (2.1a,b) is given by

Q = M - m, - m0 - m = Q0 - m = LW - m, - m0 - m (2.2) v XTI 1 2 ^ 2 ^ 1 2 TI '

where .'-M , Am-, i = 1,2,are the nuclear mass decrements.

Here, usinq the nuclear masses from ref. 1411 we calculate

the Q , when the .i° emission is accompanied by symmetric fission rr

(A1 = A2 = A/2, Zj = Z2 = Z/2) for the heavy nuclei with even

Z = 106 T 108 and A = 251 r ?10. The results for Q are given in

Table 1.

3. DYNAMICAL THRESHOLDS FOR GROUND STATE PION RADIOACTIVITY

OF THE SUPERHEAVY NUCLEI

A nuclear theory based on an exact Hatniltonian (which

includes a complete knowledge of the nuclear constituents and the

interconstituents forces) could in principle provide us a complete

explanation of all nuclear phenomena i r,c 1 ud 1 ng : fission, alpha

emission, etc., and also the ground state pion radioactivity. - 5 -

But we do not know all these ingredients in sufficient detail and then it is necessary to replace the exact Hamiltonian with a simpler oae which we can solve. Hence, recently [8-12] assuming that the pionic nuclear radioactivicy is a fission-like process in which

EJ|(nF) i E° - ran , E°(*F) " E° (3.1) we introduced the pionic f.ssility parameter

E (irF) C x m 2E o Xwc = "^ = r " ,r/ £ (3-2) 2ES(TTF) where E° , =* yZ2/A1/3, E^ = 6A2/3 are the usual Coulomb e**<$H

. and the nuclearfctCwjiA, respectively, for the spherical shape corresponding to the parent nucleus. In th€. case r ; ' that the pion rest mass is considered as originated froâ both , the electromagnetic and the nuclear one, then we can write

•% = mţj + m^ = otm^ + (1 - a)m^ , a ~ m^/m^ , (3.3a) and

F F E"C (0) = E£ - an, , E* (0) - E| - (1 - a)*, (3.3b)

c s where n, 3 am , m* = (1 -<*)"% are the contributions of the Conlomb energy and the nuclear energy to the pion rest mass.

Consequently we obtain the following general definition of the w- fissilUy parameter

F Ej (0) E° - «m, (3#4) X* F * r»Fr 2E* (0) 2lE|-(l-a)m1tl - 6 -

This is the essential parameter for the discussion of the nuclear stability with the respect to the * - fission just as in case of usu:al fission. Indeed, assuming that we si ightly deform a spherical parent nucleus into an elipsoidal one with the aid of a small symmetrical distortion of eP2(cos 8) type, then it can be shown that

F F 2 Ec (c) = E£ (0) II - I E + hioher powers of e] (3.5»)

ESF(G) = ESF(°* ll + I e2 * ni1ner powers of e] (3.5b) and therefore the total change of energy is qiven by

F F AE^ = AEJ • AEj =

F 2 F - Y- C<(0) - Ej (0)] - | e E; (0) 11 - Xj»>] (3.6)

IT F T[ F

The AEC and AE$ arr the differences between the Coulomb a'nd the surface energies for the elipsoidal and for the spherical configurations, while x|p' is the n - fissility parameter defined by eq. (3.4). Therefore, we can state that a parent nucleus (A, Z) is

F F stable toward "IT - fission" if AE* > 0 or 2Ej (0) > EJF(0) or x{^ < 1. The regions in which xj£} < 1, xj£) = 1 and xj^ >1 are presented in Fig. 1. Thus, according to a u • fission approach and using a simple liquid drop model, all parent nuclei for which *•£ > 1 ( the region indicated by open circles in Fig. 1) will be characterized by absence of a "classical" barrier (E*F(LD)) toward spontaneous pion emission from their ground state. Hence, these nuclei, which lie in the region of the superheavy elements, would be expected to emit pions in a time comparable to a nuclear - 7 -

vibrational period. The parent nuclei which lie in the region for

which X^p' < 1, Q^ > 0 (the region indicated by the sign plus in

Fig. 1) correspond to those nuclei which are able to emit pions

from their ground state only via a quantum mechanical tunel ling

through the classical "IT - fission" barrier.

It is important to note that the definition (3.4) can be used

to study any kind of pa.-ticle emission accompanied by fission if

instead of the pion rest mass m we take the average cost energy

for the production of that particle.

Certainly, one of the first things that one would line to do

with a fission-like model, or more concretely with a liquid drop model, is to find the " IT- fission" threshold and the corresponding

distortion. Therefore, as in usual fission process, the saddle

point energy is often considered to be the classical threshold

energy forn -fission. Hence the formulae [42] , which have been developed for energy and shape of the saddle point configuration

as a function of th'e usual fissility parameter xF, can be used

here for the "IT. - fission" approximation of the ground state pioir'

radioactivity by using the substitution:

V ***» Ec * EcF(°>' Es + EsF<°> (3.7)

Hence, the saddle-puint configurations and saddle point energy

(Ea ) can be given by the following six order expressions:

R(9) = RQ/A [1 + e2P2(cos 9) +eJP4(cos 9)+egP6(cos 3)1 (3.3)

where 2 3 e*=2.3333(1-X"F}-1.2262(1-x;p) +9.500(1-X™F) -

4 -8.050 9(l-x;F) + ... (3.9a)

2 3 4 c5=l.9765(l-X^F) -1.6950(l-XnF) +17.7419(l-x"F) +... (3.9b) - 8 e* = -0.9500 (1 - Xa ) + .. ( 3 • 9c ) 6 ' iiFc ' and

Ef (LD) = [E° - (1 - a)mnl '(3.10)

3 4 5 6 . [0.7 259(1-X"F) -0.3302(1-X*F) +1. 9208 (l-X"F) -0.2125(l-XjF) + ...] where the parameter A is a scale factor required to ensure that the volume remain constant at the value of a sphere of radius R .

Therefore, the "ff - fission" threshold enerqy is just the

"potential enerqy of a nucleus in the deformed confiquration at the saddle point. E* (LD) given by eq.(3.10) is in fact the liquid drop barrier height for the "^-fission" while the true

barrier height is given by

F She11 Shel1 t""-a - E^tLOa » )' - AEa .s. - AEs .p. OF)' (3-11) where AE^^^nd bt\t [*?) are the shell corrections at the qround

state and at the n - fission saddle point, respectively.

In Fig. (2a.b) we illustrate the enerqy of a fissioninq or a rc - f issioning nucleus as a function of deformation (or distance

between the fragments), while in Fig. 3 we present the saddle

point shape for the "T - fission" compared to the saddle point 236 shape for the usual fission for two parent nuclei: U and 264 [1031. In all these calculations we used the following expres- o o sions of E- and E^:

E° - 0.7053 Z2/A1/3 (3.12a)

E? » 17.9439 U-1.7826[(A - 2Z)/A]2)A2/3 (3.12b)

TTF Now, it is important to note that for the threshold energy E (LD) of the ground state pion radioactivity we have the following remarkable inequality - 9 -

F E" (LD) < E[F(LD) (3.13)

The results on the liquid drop "TT - fission" barrier E (LD), calculated using eqs. (3.10), (3.12a) and (3.12b), are presented O "If. in Fig. 4. As we can see from these results, the nucleus U 264 is stabilized as a liquid drop, while the nucleus [108] is stabilized almost completely by shell stabilization. Hence from

Figs. 1 and 4 we see that in the SHE region: Z = 112 T 120 and

F A = 260 T 300 the limits Xc = 1 and X*r = 1 (or E (LD) = 0,

E* (LO) = 0) are attained. Consequently, both phenomena "7T-fission" as well as the spontaneous fission will be essentially described by shell effects. Thus in this region the yield of the spontaneous pion emission relative to the spontaneous fission will :>e deter­ mined by the shell corrections at the ground state and at the saddle points of these two phenomena. Therefore, a detailed inves­ tigation of the competition between the ground state pionic radioactivity and ths spontaneous fission phenomena is of great interest since this competition can play an important role in determination of the true island of shel1-stabilized spherical nuci ei.

4. PREDICTIONS FOR SPONANEOUS PION EMISSION FROM SUPERHEAVY NUCLEI

The ground state pionic radioactivity (2.1a,b) 1s an extremly complex nuclear reaction in which we are dealing with a pion

emission accompanied by a rearrangement of the initial nucleus in

two final fraqments. This new type of nuclear reaction, is expected

to be a result of a combined action of the electromagnetic and

strong nuclear forces for which the Hamiltonlan is not known and

to which the perturbation theory is not applicable. Therefore, - 10 - the essence of challenge to theorist is to provide a dynamical description of thii new phenomenon within the frame work of accep­ ted theory. It is important to note that barrier penefration ".odei which is used to describe nuclear-particle emission does not appear to be applicable to long-range particle emission in fission

Isee Nobles ref. [43]] and in particular to the pionic nuclear radioactivity. However, the fission-like model introduced hy us in refs. [8-12] can be used as an intermediate step for rhe des­ cription of half-life for the pionic nuclear radioactivity in terms of the T - height, nuclear deforna lions, centrifugai barrier,etc ., just as in the case of the sionatenous fission (see Section 3). Moreover, using our fission-1 '• ke approxi­ mation, any working spontaneous fission model (e.g., liquid drop, etc.) can be extended to the spontaneous pion emission fro

The key equations on which we have estimated [8-12] the pionic radioactivity yield (?v /" <-r) are based o. the following ingredients:

(i) The "n-fission" fissility parameter given by eq. (3.2) or equivalently

Z2 (4 la) 'Z2'A>,F • Ţ • ^m - with the definitions

72 m 4 lb 9= |- -37.5; 9lfF - 9 - Y-j27J * ( - > - 11 -

(ii) An equation for the systematics of the spontaneous fission half-lives (TSF). «•

T(9) = log10TSF(9) .+ (5 - 9)fiM =

= aQ + a^ + a2d + a39 + ... (4-2)

where (5 - 9)6M is the Swiatecki's shell correction term 1441 and

ao! al* a2' a3' **•* are universa^ free parameters which can be determined by the fit of the experimental data on T^p.

(iii) The scaling law by which we assumed that the "n-fiss ion"

half-lives (T F) can be described by the same scaling function T(9),

given by e-q.f4.2) but with the substitution:

TSF<9> * T,F ' 9*9,rF <4'3>

Therefore, for the "7j-fission" phenomena we can write

*<9irF> - ^loW + <5 -9^)6* (4.4)

Then, combining eq. (4.4) with <»q.(4.2),we get

2 log1Q f~ = &9{*M + ax + a2(9 + 9^) + a3(9 +997|F+9^F)+ ...}(4.5a) SF ăff - [T(9)-1O810TSF]/(5 - 9) (4.5b)

Hence, by a two-parameter fit to the experimental values of T(9) for even-even parent nuclei, we get the following linear scaling

(LS) function [12] :

T(9) - 19.70 - 6.13 9 (4.6a)

and thje corresponding prediction for the pionic yield is given by 12

= lo T + 10 95] 9 5 (4.6b) l^[ 9lO SF - ' * where dO = IIITT/ÎA2/3. The result (4.6b) is also valid in t he general case when the pion rest mass is considered as being originated from the both energies; E£ and E?. But in this case A9 = 9 - Q^p from eq. (4.6b) is given by:

« - (1 - «)E°/E°S Ad* (4.6c) YA2/3 ' 1 - (1 -aVntr/E?

For odd-A parent nuclei the linear scaling function T(9) obtained in ref. [10] is

T(9) = 28.21 T 7 .32 9 (4.7a) and the corresponding prediction for the pionic yield is given 6y log [~1= A9 [M +. a j ] =- ||j [log T +8.39] 10 T 10 Sp

9 i 5 (4.7b)

Now, the results (4.6b) and (4.7b) car. be used for a detailed discussion of the competition between the spontaneous fission and the ground state pionic radioactivity in the region of t'ie super­ heavy elements especially for those parent nuclei for vhich the spontaneous fission half-lives are predicted. We'introduce the following conventions: the parent nuclei for which r^/IU-^ 1 will be called "SF"- , while those for which r^/r >i will be called " if''-nuclide. Also, the spontaneous fission half-life for

r s which 7T rSp will be called critical spontaneous fission half- C C -10 95 life (Tcp)- Thus for even-even parent nuclei \^ =10 yr 3 39 while for A-odd parent nuclei 1^ 10- ' yr. - 13 -

According to these defin tions from eqs . (4.6b) and (4.7b) we get the following simple rules for a rapid distinction between the "SF-" and "if-nuci ides":

(i) A parent nucleus is a "SF-nuc1 ide" if 6 > 5 and C C ' SF 4 "^S" 0r ^ ® < ^ anc' '''sF > TSF'

(II) A parent nucleus is a "nF-nucl ide" if 0 > 5 and

C C TSF > T SF or if 3 <5 and T$F < T $F .

Now, it is important to remember that, the appearance of the idea of the possible existence of superheavy elements and the theoretical predictions t24-26] of their localization around 293 the doubly magic nucleus [1141 a large number of calcula­ tions of their half-lives have been performed [27-29, 45-43J.

Rat'ier long half-lives have been obtained. For example, the spontaneous fission half-life calculated in ref. [28] for the 298 19 2 superheavy nucleus [114] is TS„F =10 ' yr and for 283 3-6 1114] is T$F = IO" yr . For these ..uclides: 9 = 6.1 for

[114] and 9 ~ 7.6 for "°[114]. Tharefore, accordinq to the rules I -11 we get that both superheavy nuclei 298[114] and 283fll4l are nuclides of "itF"-type. Moreover, using the abovt rules I and

[I and the Table I from ref. [28] we obtain (see Fig. 5) that most of nuclides from the stability island around the doubly 298 • magic nucleus [114] are nuclide of ""F" - type. A deep pionic

insta bi 1 i f,y, espec ial 1 y near the critical line, is observe) in 308 Fig. 6. Also, an island around thp nucleus [124] whert -5 T p - 10 yr is also, evidentiated in Fig. 6. The values of the

r r predicted pionic yield ( 7r/ <-r) in the case of linear scaling

(LS) are presented in Fig. 7. Detailed "-esults on the half-1 "ives

:r|-, for all superheavy nuclei with Z = 112 : 130 and N=172vl90, - 14 - are given in Table 2.

Next, it is interesting to compare these results with those oresented in Figs. 8-9 obtained from eqs. (4.5a,b) by using the nonlinear scaling (NLS) function

,2 T(8) 20.275 - 9.0358 + 0.533 9' (4.8) with Ae : A0 given by eq. (4.6c) with <* = 0.775. We note that is the scaling function (4.8)/obtained by the 3-parameters fit of the experimental data on t(9) when the errors in