Cluster disintegration

The cluster decay (also cluster emission , English cluster decay ) is a very rare type of radioactive decay . A lighter atomic nucleus is emitted, which is heavier than an alpha particle , but with 6 to 14 percent of the mass of the mother nucleus, much lighter than the typical fission fragments of nuclear fission . In addition, no neutrons are released.

So far, nuclei between carbon-14 and silicon-34 have been observed as emitted clusters. In most cases, it is not a question of the most stable nuclei according to their atomic number, but rather their isotopes with a higher neutron excess , corresponding to the neutron excess of the parent nucleus.

history

The cluster disintegration was theoretically predicted by Aureliu Săndulescu , Dorin N. Poenaru and Walter Greiner in 1980. HJ Rose and George Arnold Jones provided the first experimental evidence in 1983 at the University of Oxford , which was published in the journal Nature in early 1984 . They found that the radium isotope radium-223 (an alpha emitter with a half-life of 11.43 days) can decay directly to lead-209 with the emission of a carbon-14 atomic nucleus :

${\displaystyle \mathrm {{}_{\ 88}^{223}Ra\to {}_{\ 82}^{209}Pb+{}_{\ 6}^{14}C} }$

Type and appearance

The cluster decay has so far only been observed in some alpha-emitting radionuclides with ordinal numbers from 87 ( Francium ). Because of this occurrence of cluster and alpha decay in the same nuclide, the nuclides concerned are referred to as dual nuclear decay . In terms of nuclear physics, the cluster disintegration can be understood as a strongly asymmetrical nuclear fission.

The name "cluster" (English. Cluster , such as "lumps") was chosen because the emitted particles have an "accumulation" of more than two protons and neutrons is.

The probability of a cluster disintegration is lower by a factor of 10 ⁹ to 10 ¹⁶ compared to alpha decay . According to previous observations, the emitted clusters have a number of protons between 6 and 14. The preferred emitted clusters are carbon-14, neon-24 and magnesium-28. The ejection speed of the cluster is between 16,000 and 22,000 km / s, the recoil speed of the daughter core between 1,100 and 3,600 km / s.

cluster decay taking place	Magic number (s)	E (MeV)	${\displaystyle \lg {\frac {\mathrm {T} _{1/2}}{\mathrm {s} ec}}}$
221 Fr → 207 Tl + 14 C	N = 126; N = 8	31.292	14.52
221 Ra → 207 Pb + 14 C	Z = 82; N = 8	32.395	13.39
222 Ra → 208 Pb + 14 C	Z = 82, N = 126; N = 8	33,049	11.01
223 Ra → 209 Pb + 14 C	Z = 82; N = 8	31,828	15.20
224 Ra → 210 Pb + 14 C	Z = 82; N = 8	30.535	15.68
226 Ra → 212 Pb + 14 C	Z = 82; N = 8	28.196	21.19
223 Ac → 209 Bi + 14 C	N = 126; N = 8	33,064	12.60
223 Ac → 208 Pb + 15 N	Z = 82, N = 126; N = 8	39.473	> 14.76
225 Ac → 211 Bi + 14 C	N = 8	30.476	17.16
226 Th → 208 Pb + 18 O	Z = 82, N = 126; Z = 8	45.726	> 15.30
228 Th → 208 Pb + 20 O	Z = 82, N = 126; Z = 8	44.722	20.72
230 Th → 206 Hg + 24 Ne	N = 126	57.761	24.61
232 Th → 208 Hg + 24 Ne	-	54.509	> 29.20
232 Th → 206 Hg + 26 Ne	N = 126	55.964	> 29.20
231 Pa → 208 Pb + 23 F	Z = 82, N = 126	51.843	26.02
231 Pa → 207 Tl + 24 Ne	N = 126	60.410	23.23
230 U   → 208 Pb + 22 Ne	Z = 82, N = 126	61.387	19.57
232 U   → 208 Pb + 24 Ne	Z = 82, N = 126	62,309	21.08
232 U   → 204 Hg + 28 Mg	-	74.318	> 22.26
233 U   → 209 Pb + 24 Ne	Z = 82	60.485	24.83
233 U   → 208 Pb + 25 Ne	Z = 82, N = 126	60.776	24.84
233 U   → 205 Hg + 28 Mg	-	74.225	> 27.59
234 U   → 210 Pb + 24 Ne	Z = 82	58.825	25.92
234 U   → 208 Pb + 26 Ne	Z = 82, N = 126	59.464	25.92
234 U   → 206 Hg + 28 Mg	N = 126	74.110	27.54
235 U   → 211 Pb + 24 Ne	Z = 82	57,362	27.42
235 U   → 210 Pb + 25 Ne	Z = 82	57.756	27.42
235 U   → 207 Hg + 28 Mg	-	72.158	> 28.10
235 U   → 206 Hg + 29 Mg	N = 126	72,485	> 28.09
236 U   → 212 Pb + 24 Ne	Z = 82	55.944	> 25.90
236 U   → 210 Pb + 26 Ne	Z = 82	56.744	> 25.90
236 U   → 208 Hg + 28 Mg	-	70.564	27.58
236 U   → 206 Hg + 30 Mg	N = 126	72,303	27.58
237 Np → 207 Tl + 30 Mg	N = 126	74.818	> 26.93
236 Pu → 208 Pb + 28 Mg	Z = 82, N = 126	79.669	21.67
238 Pu → 210 Pb + 28 Mg	Z = 82	75.911	25.70
238 Pu → 208 Pb + 30 Mg	Z = 82, N = 126	76.823	25.70
238 Pu → 206 Hg + 32 Si	N = 126	76.823	25.70
240 Pu → 206 Hg + 34 Si	N = 126; N = 20	91.191	25.27
241 Am → 207 Tl + 34 Si	N = 126; N = 20	93.927	> 24.41
242 Cm → 208 Pb + 34 Si	Z = 82, N = 126; N = 20	96.510	23.15

In the Karlsruhe nuclide map from 2012, 20 radionuclides are listed which, in addition to the dominant alpha decay, also have cluster emissions:

• Francium-221 ,
• Radium-221 to 224 and 226 ,
• Actinium-223 and 225 ,
• Thorium-228 and 230 ,
• Protactinium-231 ,
• Uranium-230 and 232 to 236 ,
• Plutonium-236 and 238 and
• Curium-242 .

With some radionuclides up to four possibilities of cluster disintegration have been observed, for example three with the naturally occurring uranium isotope uranium-234: the emission of a neon-24, a neon-26 or a magnesium-28 core.

reaction	Branching ratio (%)	E (MeV)	Cluster	Speed (km / s)	Daughter core	Speed (km / s)
${\displaystyle \mathrm {{}_{\ 92}^{234}U\to {}_{\ 82}^{210}Pb+{}_{10}^{24}Ne} }$	0.9 · 10 −9	60.485	Neon 24	020,866	Lead-210	002,390
${\displaystyle \mathrm {{}_{\ 92}^{234}U\to {}_{\ 82}^{208}Pb+{}_{10}^{26}Ne} }$	0.9 · 10 −9	60.776	Neon 26	020,024	Lead-208	002,503
${\displaystyle \mathrm {{}_{\ 92}^{234}U\to {}_{\ 80}^{206}Hg+{}_{12}^{28}Mg} }$	1.4 · 10 −9	74.225	Magnesium-28	021,222	Mercury 206	002,884
For comparison: alpha decay
${\displaystyle \mathrm {{}_{\ 92}^{234}U\to {}_{\ 90}^{230}Th+\alpha } }$	≈100	04.859	Helium-4	016,567	Thorium-230	000.264

Experimentally proven cluster decays

The table on the right gives an overview of experimentally proven cluster decays with the following information:

• the cluster disintegration that takes place with the cores involved: mother core → daughter core + cluster,  

• Magic number (s) occurring as proton ( Z ) or neutron number ( N ) of the decay products ,  

• the due to the mass defect energy released E in MeV :  ,   ${\displaystyle \ \ \ E=(m_{\text{Mutterkern}}-m_{\text{Tochterkern}}-m_{\text{Cluster}})\cdot c^{2}}$

• decadic logarithm of the fictive partial half-life in seconds .  ${\displaystyle \lg \mathrm {T} _{1/2}\,/\,{\mathrm {s} ec}}$ 

Emerging cluster cores:

element	Neutron count
	133	134	135	136	137	138	139	140	141	142	143	144	145	146
87 Fr		14 C
88 Ra	14 C	14 C	14 C	14 C		14 C
89 Ac		14 C 15 N		14 C
90 th				18 O		20 O		24 Ne		24 Ne 26 Ne
91 Pa								23 F 24 Ne
92 U						22 Ne		24 Ne 28 Mg	24 Ne 25 Ne 28 Mg	24 Ne 26 Ne 28 Mg	24 Ne 25 Ne 28 Mg 29 Mg	24 Ne 26 Ne 28 Mg 30 Mg
93 Np												30 mg
94 Pu										28 mg		28 Mg 30 Mg 32 Si		34 Si
95 am														34 Si
96 cm														34 Si

Resulting daughter nuclei (mostly lead, mercury, rarely thallium, bismuth)

element	Neutron count
	133	134	135	136	137	138	139	140	141	142	143	144	145	146
87 Fr		207 Tl
88 Ra	207 Pb	208 Pb	209 Pb	210 Pb		212 Pb
89 Ac		209 Bi 208 Pb		211 Pb
90 th				208 Pb		208 Pb		206 ed		208 Hg 206 Hg
91 Pa								208 Pb 207 Tl
92 U						208 Pb		208 Pb 204 Hg	209 Pb 208 Pb 205 Hg	210 Pb 208 Pb 206 Hg	211 Pb 210 Pb 207 Hg 206 Hg	212 Pb 210 Pb 208 Hg 206 Hg
93 Np												207 Tl
94 Pu										208 Pb		210 Pb 208 Pb 206 Hg		206 ed
95 am														207 Tl
96 cm														208 Pb

literature

• Christian Beck (Ed.): Clusters in Nuclei . Volume 1 (= Lecture Notes in Physics. Volume 818). Springer, 2010, ISBN 978-3-642-13898-0 .
• Christian Beck (Ed.): Clusters in Nuclei . Volume 2 (= Lecture Notes in Physics. Volume 848). Springer, 2012, ISBN 978-3-642-24706-4 .
• Doru S. Delion: Theory of Particle and Cluster Emission . (= Lecture Notes in Physics. Volume 819). Springer, 2010, ISBN 978-3-642-14405-9 .

Individual evidence

1. ↑ Aureliu Săndulescu, Dorin N. Poenaru, Walter Greiner: New type of decay of heavy nuclei intermediate between fission and a decay. In: Soviet Journal of Particles and Nuclei. Volume 11, number 6, 1980, p. 528 (= Fizika Elementarnykh Chastits i Atomnoya Yadra ). Volume 11, 1980, p. 1334.
2. ^ HJ Rose, GA Jones: A new kind of natural radioactivity. In: Nature. Volume 307, Number 5948, January 19, 1984, pp. 245-247 doi: 10.1038 / 307245a0 .
3. ↑ K. Bethge, G. Walter. W. Wiedemann: Nuclear Physics. 2nd Edition. Springer 2001, ISBN 3-540-41444-4 , p. 236.
4. ^ KH Lieser: Nuclear and Radiochemistry. 2001, ISBN 3-527-30317-0 , p. 67.
5. ^ J. Magill, G. Pfennig, R. Dreher, Z. Sóti: Karlsruher Nuklidkarte. 8th edition. 2012. Nucleonica GmbH, 2012, ISBN 978-92-79-02431-3 (wall map) or ISBN 978-3-00-038392-2 (folding map).
6. ↑ KP Santhosh, B. Priyanka, MS Unnikrishnan: Cluster decay half lives of trans-lead nuclei within the Coulomb and proximity potential model. In: Nuclear Physics A. Volume 889, 2012, pp. 29-50, doi: 10.1016 / j.nuclphysa.2012.07.002 , arxiv : 1207.4384 .
7. ^ Attila Vértes, Sándor Nagy, Zoltán Klencsár, Rezso György Lovas (eds.): Handbook of Nuclear Chemistry. Vol. 1: Basics of Nuclear Science. 2nd Edition. Springer, 2010, ISBN 978-1-4419-0719-6 , pp. 840-841.
8. ↑ DN Poenaru, Y. Nagame, RA Gherghescu, W. Greiner: Systematics of cluster decay modes. In: Physical Review C. Volume 65, number 4, 2002, p. 054308, doi: 10.1103 / PhysRevC.65.054308 .
9. ↑ DN Poenaru, Y. Nagame, RA Gherghescu, W. Greiner: Erratum: Systematics of cluster decay modes, [Phys. Rev. C 65, 2002, p. 054308]. In: Physical Review C. Volume 66, number 4, 2002, p. 049902 (E), doi: 10.1103 / PhysRevC.66.049902 .

Web links

• Literature review
• DN Poenaru, W. Greiner: Cluster radioactivity - past, present and future. Workshop on State of the Art in Nuclear Cluster Physics, May 13-16, 2008, Strasbourg ( theory.nipne.ro PDF, 52 pages).