Spontaneous pion emission as a new natural radioactivity

ANNALS OF PHYSICS 171, 237-252 (1986)

Spontaneous Pion Emission as a New Natural Radioactivity

D. B. ION AND M. IVASCU

Institute for Physics and Nuclear Engineering, Bucharest, P. 0. Bou MG-6. Romania

AND

R. ION-MIHAI

Bucharest University, Faculty of Physics, Department of Nuclear Physics. Bucharest, Romania

Received August 12, 1985

In this paper the pionic nuclear radioactivity or spontaneous pion emission by a nucleus from its ground state is investigated. The Q,-values as well as the statistical factors are calculated using the experimental masses tabulated by Wapstra and Audi. Then it was shown that the pionic radioactivity of the nuclear ground state is energetically possible via three-body channels for all nuclides with 2 > 80. This new type of natural radioactivity is statistically favored especially for 2 = 92 ~ 106 for which F,/F,, = 40 - 200 [MeV]*. Experimental detection of the neutral pion and also some possible emission mechanisms are discussed. C 1986 Academic Press, Inc

1. INTRODUCTION

The last years have been fruitful with the first reports of the ground state proton radioactivity [ 11, j?-delayed-2p decay [2], P-delayed-3H decay [3], 14C radioactivity [48] and Ne radioactivity [S-lo]. Thus, the radioactivity includes actually two types: (i) spontaneous emission of elementary particles, such as y, electron, positron, proton, and neutron [ 11, 121, (ii) spontaneous emission of nuclear clusters, e.g., a, 14C, Ne, j?-delayed-2p decay, /Ldelayed-2n decay, and in general spontaneous fission from symmetric fission up to very asymmetric fission.

In this paper we investigate the pionic nuclear radioactivity, or spontaneous emission of pions from the ground state of a nucleus, as a new, very fascinating, and quite different from types (i)-(ii) decay mode, possible only via 3-body final state channels. Thus, in Section 2, the Q,-values are calculated using the masses tabulated by Wapstra and Audi. Then it is shown that the pionic radioactivity is energetically possible for all nuclides with Z> 80. The most convenable inden- tilication of the spontaneous emission of the neutral pions can be made by detecting

237 0003-4916/86 $7.50

Copyright Q 1986 by Academic Press. Inc. AU rights of reproduction in any form reserved.

238 ION, IVASCU, AND ION-MIHAI

the two y rays from the dominant decay mode rc” + 2y using the B-glass Cherenkov-detector telescopes. The values of the minimum opening angle between the two telescopes (or between two y rays), for some no-emitters of experimental interest, are given in Section 2. The decay width f,, statistical factors F,/Fs, as well as the statistical energy distributions are discussed in Section 3. Some possible mehanisms for the pionic radioactivity and the conclusions are presented in Sec- tion 4.

2. Q,-SYSTEMATICS AND DETECTION OF PIONIC NUCLEAR RADIOACTIVITY

The spontaneous emission of pions from a ground state nucleus via two-body final state decay mode

LAz)+(AZ,)+% z=z, +z, (2.1)

is forbidden because of the conservation of energy and momentum. To liberate the pions (the quanta of nuclear forces) as free particles, sufficient energy must be imparted to the nucleus to create their rest mass [mno = 134,9626 MeV, rn,* = 139,5669 MeV]. So, we must try to understand, at least in a qualitative way, how the nucleus can emit spontaneously a real pion or if the spontaneous emission is energetically possible from a ground state nucleus via a 3-body or a 4-body decay mode. Thus, we start our discussion with a reaction

(2.2a)

with

A =A, +A,, z=z, +z2 +z, (2.2b)

where A, A,, Az and Z, Z,, Z2 are the usual mass and charge numbers of the involved nuclei while Z, denotes the charge of a pion. If the nuclear masses, M(A, Z) = A4, M(A,, Z,) z m,, M(Az, Z2) = m,, and also the pion rest mass m,, are given in units of energy, then the total energy liberated in the reaction (2.2a), (2.2b) is

Q, =M--m, -m2 -m, =AM--Am, -Am, -m, (2.3)

where AA4 = M - A, Am, = mi - A I, i = 1,2, are the nuclear mass decrements (see Fig. 1).

The energy condition for the spontaneous emission of a pion from a ground state nucleus is Q, > 0. This condition can be fulfilled by nuclei for which AM > 0 and Ami < 0, i = 1,2. Indeed, from a close examination of the mass decrements presented in Fig. 1, we see that AM > 0 for all nuclides with Z < 82. Thus, Qn > 0 for all final state transitions in the region of symmetric fission (Z, = Z, = Z/2;

PIONIC RADIOACTIVITY 239

FIG. 1. Mass-decrements (d = M- A) for the nuclei tabulated by Wapstra and Audi [14] as function of Z.

A I = AI = A/2). In fact the range of nuclides energetically able to emit n-mesons from their ground state can be derived from a consideration of the semiemperical mass formula, e.g.,

M(Z, A)=~,Z+~,(A-Z)-~,A+U.,A*‘~

Z’ + a(, A’/3 + atI

(A-22)‘+S A P (2.4)

where, the pairing-energy 6, = a,A - 3/4 for odd-odd nuclei, 6, = 0 for odd-even and even-odd nuclei, and 6, = -a,Ae314 for even-even nuclei, and [ 131: av = 14.1 MeV; a, = 13 MeV; a,, = 0.595 MeV; a(, = 19 MeV; and ap = 33.5 MeV. Then, for the special case of the pion spontaneous emission accompanied by symmetric fission (A, = A, = A/2; Z1 = Zz = Z/2) we have

Qn = -m, - 3.3787 Azi3 + 0.2202 $ + qp (2.5)

whre qp = -79.18 A 3’4 MeV for odd-odd nuclei, qp = 0 for evenodd and odd-even nuclei, and qp = 79.18 A - 3’4 for even-even nuclei. Therefore, neglecting small pairing contribution qp, the three terms which make up the value of Q, originate from the Coulomb energy which is set free, the surface energy, and the pion mass which has to be supplied. Hence, for the nucleus 235U, Q, obtained with Eq. (2.5) is Qn = 38 MeV which is an energy sufficient for the emission of a real pion with a kinetic energy up to 38 MeV. Since semiempirical mass formula (2.4) as well as other mass formulae can induce large errors in the estimation of total energy liberated in the reaction (2.2), here we have calculated Qn by using the known masses tabulated by Wapstra and Audi [14] in which are included the shell effects, pairing corrections, etc. Thus, the results given in Fig. 2 illustrate the fact that the


-fOll- ( J , , , , , , ,y

180 200 220 240 260

Fig 2 --A

FIG. 2. The Q,-intervals for the spontaneous #-emission accompanied by charge-symmetric fragmentation (2, = Z, = Z/2). The intervals [em”‘, Qy] for each fixed Z correspond to those pionic decay modes for which there exist masses tabulated by Wapstra and Audi [14].

pion spontaneous emission from the ground state is energetically possible for all nuclides with Z= 80 + 106. In fact, in Fig. 2, we have indicated only the intervals [emin, Q”““] obtained in the reaction of type

(A, Z) + (A I, -ml + (AZ. Z/2) + no (2.6)

for each possible no-emitter (A, Z) with Z = 80 + 106. Detailed Q,-values are given in Figs. 3-6 only for the following energetically possible exclusive reactions

Hg+Zr+Zr+rr’ (2.7a)

Pb-Nb+Nb+n’ (2.7b)

Rn-+Tc+Tc+n’ (2.7~)

Cf-+In+In+z’. (2.7d) I ““”

-A Zr

FIG. 3. The Q,-values for each Hg possible no-emitter with A odd for A = 175 -205. Only the charge-symmetric decay modes (Z, =Z, =40), with AZ, for which there exist masses tabulated by Wapstra and Audi [14], were taken into account. The solid lines are drawn to guide the eye.


FIG. 4. The Q,-values for each Pb possible no-emitter with A odd for A = 183 + 209. Only the charge-symmetric decay modes (Z, =Z, =41), with A,, for which there exist masses tabulated by Wapstra and Audi [ 141, were taken into account. The solid lines are drawn to guide the eye.

FIG. 5. The Q,-values for each Rn possible no-emitter for A = 199 t 213. Only the charge-symmetric decay modes (2, = Zz = 43), which ATc for which there exists masses tabulated by Wapstra and Audi [14], were taken into account. The solid lines are drawn to guide the eye.


FIG. 6. The Q,-values for each Cf possible #-emitter for A = 239 + 253. Only the charge-symmetric decay modes (Z, = Z, = 49), with A,, for which there exists masses tabulated by Wapstra and Audi 1141, were taken into account. The solid lines are drawn to guide the eye.

Then, we see that Qmax is obtained for the pion emission accompanied by symmetric fragmentation modes A, N Al = A/2, Zr z Zz = Z/2 of the initial nucleus.

Next, in Figs. 7-8, we have presented Q,(Ax, Z,)-values for the pion radioactivity of some nuclides [e.g., 232U, 242Pu, 250Cm, 254Cf, for all their pionic decay modes for which there exist masses given in Wapstra and Audi [ 141. Then, we see

0 20 40 CHARGE OF LIGHTh?AGMENT

FIG. 7. The Q-values for all rr’ decay modes of *‘?U, tsoCm and z42Pu, for which there exists masses tabulated by Wapstra and Audi [14]. The solid curve is drawn to guide the eye.


FIG. 8. The Q,-values for all (n-, no, n+)-decay modes of ““Cf. for which by Wapstra and Audi [14]. The solid curve is drawn to guide the eye.

CHARGE OF LIGHT FRAGMENT

there exists

that the pionic spontaneous emission is energetically possible only in the region of near symmetric fragmentation of the initial nucleus while the Q-values are negative for the very assymmetric fragmentation modes. Then, the most convenable detection of the pionic nuclear radioactivity can be made in the inclusive measurements of 7r0-mesons.

Neutral pions decay with 98.85% probability into two y rays, on a time scale of 0.828 x lo-16s and consequently no-radioactivity could be experimentally determined by y rays as well as by the presence of the nuclear fragments in the range of low kinetic energies below Q,-values. Thus, neutral pions spontaneously emitted by a nucleus from its ground state can be identified by detecting the two y-rays in an array of Pb-glass Cherenkov-detector telescopes. High-energy y rays will be converted into the electromagnetic showers and then using photomultipliers one can detect the Cherenkov light produced by these showers. During the experiment, energy thresholds will be set for each detector and events of twofold or higher coin- cidences between any combination of telescopes will be selected. Next, twofold coin- cidence events will be sorted into Z-dimensional array of invariant mass

rn$ = [(Pi,, + Pp2)2]1’2 = 2(Ei., J!$)“‘~ sin[q/2] (2.8)

versus opening angle cp between the two telescopes (i.e., between the two y rays). Invariant mass m,*o for true no events should be distributed around of the no rest mass with a width determined by the y-ray energy and the angular resolution of the telescopes. The opening angle cp, corresponding to 7~’ kinetic energies between QK and 0 MeV, should fall in the range cpO d cp < 180°, where

q. = 2 sin-‘[m,o/(m,o + Q$F)]. (2.9)

The values of Qa and the minimum opening angle cpo between the two telescopes, for some no-emitters of experimental interest, are given in Table I.


TABLE I

The Values of Qy, ‘p,,. and (F,/FsF)max for Each #-Emitter with Even Z= 90 t 106

CPO F,/FsF Z A ZI A, Oy(MeV) (degrees) (MeV)*

1 2 3 4 5 6 I

92

(U)

94

(Pu)

212 45 105 51.79 92.6 32.06 213 45 106 50.35 93.5 30.42 214 45 107 49.41 94.1 29.37 215 45 107 47.91 95.1 27.73 216 45 107 47.29 95.6 27.06 217 45 108 47.35 95.5 27.13 218 45 109 45.54 95.4 27.33 219 45 108 46.97 95.8 26.72 220 45 109 47.10 95.1 26.86 221 45 110 47.22 95.6 26.99 222 45 111 46.91 95.8 26.66 223 45 111 46.54 96.1 26.26 224 45 111 46.22 96.3 25.93 225 45 112 46.10 96.4 25.80 226 45 113 45.97 96.5 25.67

226 46 112 62.16 86.4 44.96 227 46 113 61.10 87.0 43.56 228 46 114 61.35 86.9 43.89 229 46 114 60.29 87.5 42.50

230 46 114 60.29 87.5 42.50 231 46 116 59.91 87.7 42.01

231 47 115 71.22 81.8 57.72 232 47 115 70.66 82.0 56.89 233 47 116 70.10 82.3 56.64 234 47 117 69.85 82.4 55.70 235 47 117 69.04 82.8 54.52 236 41 117 68.85 83.9 54.25 231 47 118 68.35 83.2 53.53 238 47 119 68.47 83.1 53.71 239 47 119 68.09 83.3 53.17 241 47 120 68.35 83.2 51.22 242 47 121 68.85 83.4 54.25

Table conrimed


TABLE I-Continued

1 2 3 -

4 5 6

96 235 48 117 86.22 15.2 81.68

(Cm) 236 48 118 86.35 15.2 81.90 231 48 118 84.45 75.8 19.35 238 48 118 85.16 75.6 79.87 239 48 119 84.10 16.1 78.08 240 48 118 83.91 76.1 77.87 241 48 120 83.12 76.2 77.45 242 48 120 84.47 15.9 75.78 243 48 121 83.79 16.2 17.56 244 48 122 84.79 75.8 79.24 245 48 122 84.04 76.1 77.98 246 48 123 82.41 76.8 75.27

98 239

(Cf) 240 241 242 243 244 245 246 241 248 249 250 251 252 253 254

49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49

50 50 50 50 50 50 50 50 50 50 50 50

119 96.85 71.2 100.67 119 96.66 71.3 100.32 120 95.85 71.6 98.81 121 96.10 71.5 99.28 121 95.41 71.7 98.01 121 95.35 71.7 97.89 122 95.54 71.7 98.24 123 96.04 71.5 99.16 123 95.66 71.6 98.46 123 96.16 71.5 99.39 124 96.29 71.5 99.62 125 97.10 71.1 101.13 125 97.41 71.0 101.83 125 98.60 70.6 103.95 126 99.16 70.4 105.01 127 100.97 69.9 105.51

246 247 248 249 250 251 252 253 254 255 256 257

122 113.47 65.8 133.50 123 112.66 66.1 131.81 124 113.41 65.8 133.07 124 112.79 66.0 132.07 124 113.41 65.8 133.37 125 113.10 65.9 132.72 126 114.04 65.6 134.67 126 113.97 65.8 134.54 126 115.30 65.3 137.30 127 115.66 65.2 138.09 128 117.10 65.7 141.14 128 117.60 65.6 142.21

Table continued

246 ION,IVASCU, AND ION-MIHAI

TABLE I-Conrinued

1 2 3 4 5 6 I

102 (NoI

104

106

251 51 125 122.60 63.2 153.05 252 51 125 122.97 63.1 153.88 253 51 126 122.54 63.2 153.91 254 51 121 123.22 63.0 154.43 255 51 127 123.22 63.0 154.43 256 51 127 124.29 62.7 156.78 251 51 128 124.53 62.7 157.34 258 51 129 125.85 62.3 160.27 259 51 129 126.16 62.2 160.97

255 52 127 136.54 59.6 184.90 256 52 128 137.16 59.5 186.39 257 52 128 136.91 59.5 185.79 258 52 128 137.66 59.3 187.57 259 52 129 137.99 59.3 187.87

260 52 130 138.79 59.1 190.26 261 52 130 138.85 59.1 190.41

260 52 129 147.97 57.0 212.75 261 53 130 147.66 57.0 211.96 262 53 131 148.47 56.9 214.00 263 53 131 148.35 56.9 213.69

Note. Only the charge-symmetric decay modes (Z, = Z, = Z/2) for which there exists masses tabulated by Wapstra and Audi 1141 are taken into account.

3. DEFINITION OF THE WIDTH AND STATISTICAL FACTORS FOR SPONTANEOUS PION EMISSION

In the treatment of the spontaneous emission of pions from a ground state nucleus, we are often faced with a phenomenon for which the law of interaction is unknown. We expect that this phenomenon is a result of combined action of the electromagnetic and strong nuclear forces for which the Hamiltonian is not known and to which perturbation theory is probably not applicable. Then, it often becomes useful to assume that the transition probability is simply proportional to the number of final quantum state available for the process under consideration. This hypothesis is specific to the so called “statistical moder’ which was proposed by Fermi [ 151 as a simple model of particle production in strong interactions. In the experimental analysis of a single channel, such a model is often very useful, since it allows an approximate separation between the kinematical and dynamical effects. The computation of statistical factors provides us at least with the first guide in our attempts to investigate the spontaneous pion emission phenomena.


Therefore, for comparison let us consider the 2-body spontaneous fission (SF) process

(A,Z)~(A,,Z,)+(A2,Z*). (3.1)

The spontaneous 2-body fission “width” rSF as well as the spontaneous pion emission “width” r, can be written as

~su=~~l~s~!‘dLi~~(~2,P,,~2)i (3.21

~~=~jIT~I’dLips(M’,P,,P,,P,i, (3.3)

where TsF = (AIZ,; A2Z2 ) TJ AZ) and T, = (A,Z,; A2Z2; rc ) TJ AZ) are the invariant transition amplitudes for the spontaneous fission and the spontaneous pion emission, respectively. dLips(M’, P,, P2) and dLips(M’, P,, P,, P,) are the 2-body and 3-body final state Lorentz invariant phase space (Lips) elements [16] in which P, = (p,, E,) and Pi = (p,, Ei), i= 1,2 are the 4-momenta of the initial and final particles, while M, mi, i = 1, 2, 71, are their rest masses. These phase space elements, in the rest frame of the initial decaying nucleus (A, Z), after cancelation of all b-functions. become

dLips(M’, P12 P2) = t2nJ2 i= ,,2 1 n d4Pi &Pi -mf) h4(P- P, - Pz)

PCM dQ =p, dQ=dcosBdp 167~~

(3.4a)

pCM=&lM2-(m, -m# IM2-(m, +n12)21”’ (3.4b)

dbsW2, 6, p2, PJ = (2n)S i= ,,2,n 1 n d4P, 6(Pf-mf)64(P-P, -P, -P,)

= $ dE, dE, O(X) (3.5a)

A’-4[Ef--m:][E~-m,2- [M2-2M(E, +E,)+2E,E, +mf+mf-mm:]’ (3.5b)

where 8 and cp are the c.m. polar and azimuthal angle in the reaction (3.1) while O(X) is the Heaviside step function. Therefore, in a reaction (2.2), each event can be plotted as a point in (E,, E,)-plane. This is called a Dalitz plot [ 17, IS]. In the cm. system of reaction (2.2) the condition p1 + p2 + pn =0 means that these momenta are coplanar. So, the limiting curve of the Dalitz plot corresponds to events which are colinear [(q - mf)‘12 + (E$ - rni)l” f (Ez - mi)“* = 0] and then the equation for the Dalitz curve is X= 0 (see Eq. 3.5b), since E, = M-E, -E,.


Next, using Eqs. (3.2), (3.3), (3.4a), and (3.5a) we obtain

r F n=).n r FSF (3.6)

SF

FsF. = & Lips(M2, m,, m2) = s

Fn = &Lips(M*, ml, m2, m,) = 256i3M3~,

(3.7)

(3.8a)

I I ,~~~~I~ $ [M2 _ (m, - x1/2)21 112

. [M2- (m, +~“~)~]“~[x-(m, +m,)2]‘/2[x- (ml -m,)2]1’2 (3.8b

I(A,Z*;‘42Z,;~ IT, I AnI:,.

r= I(A,Z,;A,Z, IG.FI~Z)I~“.

I~~,~,;~2~2;~l~,I~~~l~,.

= j I T, I2 dLbW2, PIT p2, p,)

j dLips(M2, PI, P,, P,)

I(A,,Z,;A~Z~ITSFIAZ)I~~.

= s I Ts, I 2 dLips(M2, PI, P2)

j dLips(M*, P, , P2)

(3.9a

(3.9b)

(3.9c)

The quantities Fz and FSF will be called Lorentz invariant statistical factors. In Fig. 9 we have presented the values of the intervals [(F,/FSF)min, (F,/FSF)max]

for all possible no-emitters with even Z = 80 t 106 and different A. For each nuclide with Z and A fixed we have taken into account all the channels (2.2) and (3.1) with

-A

FIG. 9. The (F,/Fs,)-intervals for the spontaneous @-emission accompanied by charge-symmetric fragmentation (Z, =Z, =Z/2). Only those decay modes, for which there exist masses tabulated by Wapstra and Audi [14], were taken into account.


2, = Z2 = Z/2 and different A, and Az for which the masses are tabulated in Wapstra and Audi [ 141. Some numerical values of (F,/FsF),,, are given in Table I. Detailed values of the branching ratios F,JFsF are given in Figs. 10-12 for all the no-emitters of types Cf, Fm, and No, respectively.

Next, with the assumption that

I(AIZI;A,Z,;~I ~,I~~~12=I~~,~,;~2~2;~l LIAZ)I:,. (3.10)

one can calculate the energy distribution of the emitted pions. Then, we obtain

dr, I(~,ZI;~,Z~;~/T,I~Z)I~,,

do= 128n3M2

x f [S1* -(m, -m,)*]“*[S,, -(m, +mJ2]“2 12

x [M2-((S~~*-mm,)*]“*[M2-(S”*+m )*]l’*, I2 n (3.11)

where the pion kinetic energy o is connected with the invariant mass S,, of the final nuclear fragments by the relation

S12 =(M-m,)*-2A4o. (3.12)

In any case, we think that it is premature to speculate on any emission mechanism before a detailed comparison of the result (3.11) with the experimental data.

FIG. 10. The statistical branching F,/F,, [MeV] 2 for each Cf possible no-emitter with A = 239 + 254. Only the charge-symmetric decay modes (2, = Z, = 49), with A,, for which there exist masses tabulated by Wapstra and Audi [14], were taken into account. The solid lines are drawn to guide the eye.


FIG. 11. The statistical branching ratio F,/F sr [MeV]’ for each Fm possible no-emitter with A = 251 t 259. Only the charge-symmetric decay modes (Z, = Zz = 50) for which there exist masses tabulated by Wapstra and Audi [14], were taken into account. The solid lines are drawn to guide the eye.

FIG. 12. The statistical branching ratio F,/F sF [MeV]’ for each No possible #-emitter with A = 246 + 257. Only the charge-symmetric decay modes (Z, = Z, = 51) for which there exist masses tabulated by Wapstra and Audi [ 141 were taken into account. The solid lines are drawn to guide the eye.


4. DISCUSSION AND CONCLUSIONS

In this paper we have introduced the pionic nuclear radioactivity or spontaneous pion emission by a nucleus from its ground state as a new type of natural radioactivity which is possible via 3-body final state. So, since the spontaneous pion emission (2.2a), (2.2b) is an extremely complex reaction in which we are dealing with a pion production and a rearrangement of the initial nucleus into two nuclei, we attempt to describe it as a 2-step process. Thus, the initial nucleus, by pion emission, must pass through a transition state (of meanlife T >/ fiQ; ‘) in which almost all its forms of internal energies have been converted into the production of a pion with a given total energy and also into potential energy of deformation. In this transition state the nucleus is very cold and only a few well defined quantum states are available to it. We expect that these states will have considerable defor- mations. Thus, the initial nucleus, after pion emission, can pass through only those very few available transition states which have proper total angular momentum and parity. Then, the term of coldfission channel can be associated with these transition states and each of cold fission channels can subsequently lead to the formation of a whole spectrum of fragments (A,, Z,) and (Al, Z,) associated in the pion emission (2.2a), (2.2b). We note, of course, that other alternative 2-step mechanisms can be proposed for the spontaneous pion emission, e.g., after a near symmetric (A i 1: A, N A/2, Z, N Z, N Z/2) spontaneous cold fission one of the final fragments is an exotic nuclear DDR state [ 19-211, with mean lifetime 5 Z fiQ- ‘, which is decaying via pion emission.

All these mechanisms can be used as intermediate steps for the determination of halflife for pionic nuclear decay by using the potential barrier, nuclear deformation, centrifugal barrier, and spectroscopic factors. We note at this stage an accurate estimate of T(A -+ TEA, A,) is impossible. However, in the above 2-step mechanism, an estimation of the hindrance factor in a Gamow-like model for T(A -+ nA*) lead to a value of the order of unity for the neutral pion emission. To estimate the various contributions it is first necessary to discover and study a number of pionic radioactive nuclides in different regions of nuclidic chart.

The model independent results as well as the conclusions may summarized as follows:

(i) The pionic radioactivity of nuclear ground state is energetically possible (Q, > 0) via 3-body channels (see Figs. 2-8) for all nuclides with Z > 80;

(ii) The pionic spontaneous emission is statistically favored especially for Z = 92 t 106 (see Figs. 9-12 and Table I) for which F,/F,, = 40 t 200 [MeV]‘;

(iii) Neutral pions can be inclusively measured by detecting the two high energy y rays using Pb-glass Cherenkov-detector telescopes. The values of minimum angle between the two y rays (or minimum opening angle between the two telescopes), for some no-emitters of experimental interest are given in Table I;

(iv) The width r,, the statistical factor Fn/FsF and the statistical energy dis-

595/171:2-2


tribution of the emitted pions are given by Eqs. (3.3) (3.5a), (3.3b), (3.7) (3.8a), (3.3b), and (3.11), respectively.

All these results provide us with the first guide in our attempts to investigate and interpret the spontaneous pion emission phenomena.

Finally, we note that a number of experimental facts can be considered as experimental indications in favor of the spontaneous emission from the nuclear ground state. These are (a) the existence of a gap in the mass distributions in the region of the symmetric spontaneous fission, (b) the discovery of the subthreshold pion production phenomena [22-281, and (c) the pionic fusion near the threshold ~291.

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Spontaneous pion emission as a new natural radioactivity

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