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S. A. Karamian

I. Elementary microscopic states of complex nuclei are manifested:

• in radioactive decay processes;

•• in specific nuclear reactions as: a) Scattering;

b) Coulomb excitation; c) Stripping reactions.

TO THE MECHANISM OF PARTICLE TO THE MECHANISM OF PARTICLE RELEASE IN NUCLEAR REACTIONSRELEASE IN NUCLEAR REACTIONS

Joint Institute for Nuclear Research, Dubna, Moscow region, Russian Federation

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II. Bulk reactions proceed via continuum of excited levels being treated within statistical and macroscopic approaches. Among them could belisted the most abundant processes as:

• Compound nucleus formation and decay;

•• Fission;

••• Nucleon emission from highly excited nuclei, and so on.

III. In statistical model, the nucleus is characterized by temperature, entropy and total angular momentum. All nucleons are assumed identical and their individual quantum numbers make no significance.

IV. It would be yet interesting to deduce the status of nucleons inside a nuclear volume from the data reached in reaction experiments.

V. Some examples of intrinsic structure manifestation are given below.

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I. Observation of low probability for (, α) reactions that requires the pre-formation factor. Conclusion: α-clusters and multi-quark objects may be present in nucleus but with low probability ~10–2;

II. In reactions with heavy ions, the probability of α emission is oppositely very high. Conclusion: alphas are formed through the special mechanism of internal coalescence;

III. Observation of an excess in the Tl values for emission of neutrons with l ≥3 at INNA experiment. Internal single nucleon orbits possess a high momentum, but centrifugal barrier suppresses their emission. The re-arrangement of orbits is needed. The enhanced yield of INNA means an effect of internal states;

MANIFESTATION OF INTERNAL STATES IN MANIFESTATION OF INTERNAL STATES IN REACTIONS OF STATISTICAL MECHANISMREACTIONS OF STATISTICAL MECHANISM

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IV. Observation of the preferential population of high-spin states in (, n) and (, p) reactions with isomeric targets. Survival of the structure selectivity indicates incomplete mixing of specific states even despite excitation energy of E* ≈ 7-15 MeV;

V. The re-arrangement of internal states in advance of particle emission suppresses the absolute reaction rate as compared to the standard statistical estimates.

VI. Some major details are given below.

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REFERENCES TO THE ORIGINAL WORKSREFERENCES TO THE ORIGINAL WORKS

I. Reactions induced by 23 MeV bremsstrahlung

Ref. [1]: S.A. Karamian, “Threshold and spin factors in the yield of

bremsstrahlung-induced reactions”. Preprint JINR, E15-2012-65,

Dubna, to be published in Phys. of Atomic Nuclei.

Ref. [2]: S.A. Karamian, “Yield of bremsstrahlung-induced reactions as

a probe of nucleon-nucleon correlations in heavy nuclei”. In: Proc. of 4-

th Intern. Conf. NPAE-2012, p. 141, Kiev, Ukraine.

Ref. [3]: S.A. Karamian, “To the mechanism of alpha particle emission

induced by photons”. Submitted to Phys. Lett. B (2013).

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II. Inelastic acceleration of thermal neutrons by isomers

Ref. [4]: S.A. Karamian and J.J. Carroll, “Cross section for inelastic

neutron “acceleration” by 178m2Hf”. Phys. Rev. C (2011) v. 83, p.

024604.

Ref. [5]: O. Roig, G. Belier, et al., “Evidence for inelastic neutron

acceleration by the 177Lu isomer”. Phys. Rev. C (2006) v. 74, p.

054604.

Ref. [6]. S.A. Karamian, A.G. Belov, et al., “Upper limit for 180mTa

depletion by neutrons”. In: Book of Abstracts of 63d Conf. on Nucl.

Spectroscopy, Science, St-Petersburg, 2013.

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THRESHOLD DEPENDENCE OF THE (THRESHOLD DEPENDENCE OF THE (,n) AND (,n) AND (,p) ,p) REACTION YIELDSREACTION YIELDS

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• To systematize the spin dependence, the yields are plotted as a function of a new parameter:

[Im(Im +1) – It(It + 1) ],

where Im and It are the spin values for the product isomer and the target nucleus. Choice of this parameter is very natural, despite somewhat new and original.

• The process probability in thermodynamics approach must be proportional to a number of microstates at definite thermal energy. Let’s remind the nuclear level density anzatz:

• This equation practically includes the subtraction of the rotational energy Erot ~ I(I + 1) from total excitation E* in order to get the thermal energy Etherm = E* - Erot. The rotational energy could be considered as a form of kinetic energy.

SPIN-DEPENDENCE: ISOMER YIELDSSPIN-DEPENDENCE: ISOMER YIELDS

.σ2

)1( exp

σ

)12( *)(ρ)*,(ρ

23

IIIEIE

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SYSTEMATIC OF YIELDS VERSUS “SPIN PARAMETER”SYSTEMATIC OF YIELDS VERSUS “SPIN PARAMETER”

179Hf (,p)178mLu

9/2 9

178m2Hf (,n)177m2Hf 16 37/2

180mTa (,p)179m2Hf 9 25/2

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ENCOUNTER DATA FOR THE (ENCOUNTER DATA FOR THE (, α) EXPERIMENT, α) EXPERIMENT

Target Abundance, % Product Halflife E, keV Background

109Ag 48.2 105Rh 35.4 h 319 105Ag from (γ, 2n)

113Cd 12.2 109Pd 13.7 h 88 109Cd from (γ, n)

115In 95.7 111Ag 7.45 d 342 –

119Sn 8.6 115Cd 53.4 h 528 –

137Ba 11.2 133Xe 5.25 d 81 133mBa from (γ, n)

143Nd 12.2 139Ce 138 d 166 –

145Nd 8.3 141Ce 32.5 d 145 141Nd from (γ, n)

153Eu 52.2 149Pm 53.1 h 286 149Eu from (γ, 2n)

160Gd 21.9 156Sm 9.4 h 204 –

163Dy 24.9 159Gd 18.5 h 364 159Dy from (γ, n)

176Yb 12.8 172Er 49.3 h 407 –

176Lu 2.6 172Tm 63.6 h 1094 172Lu from (γ, 3n)

181Ta 100 177Lu 6.65 d 208 –

187Re 62.6 183Ta 5.1 d 246 183Re from (γ, 2n)

193Ir 62.7 189Re 24.3 h 245 189Ir from (γ, 2n)

203Tl 29.5 199Au 75.3 h 158 –

207Pb 22.1 203Hg 46.6 d 279 203Pb from (γ, n)

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EXPERIMENTAL RESULTS FOR THE YIELD OF (EXPERIMENTAL RESULTS FOR THE YIELD OF (, , ) REACTIONS) REACTIONS

Target Product Halflife E, keV Relative yield: (,)/(,n)

Threshold parameter: (Eth+Bc), MeV

109Ag 105Rh 35.4 h 319 (1.5 ±0.3)·10–4 13.56

113Cd 109Pd 13.7 h 88 (2.4±0.3)·10–4 14.32

115In 111Ag 7.45 d 342 (4.5±0.5)·10–5 14.45

119Sn 115Cd 53.46 h 528 (3.9 ±0.4)·10–5 15.31

176Yb 172Er 49.3 h 407 (0.4 ±0.1)·10–5 14.75

181Ta 177Lu 6.65 d 208 (0.70 ±0.12)·10–5 14.51

193Ir 189Re 24.3 h 245 ≤ 2.8·10–4 15.84

207Pb 203Hg 46.6 d 279 (1.7±0.2) ·10–6 17.51

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MEASURED YIELDS OF THE (MEASURED YIELDS OF THE (, , pp) REACTIONS) REACTIONS

Target Reaction Product Halflife E, keV Relative yield:(, p)/(,n)

(Eth+Bc),

MeV

natCd 112Cd (, p) 111Ag 7.45 d 342 (1.15±0.15)10–2 14.83

113Cd (, p) 112Ag 3.12 h 617 (1.00±0.15)10–2 14.89

114Cd (, p) 113Ag 5.37 h 299 (0.98±0.15)10–2 15.40

natSn 118Sn (, p) 117gIn 43.2 min 553(4.9±0.5)10–3

15.4215.74117mIn 116 min 315

116Sn (, p) 115mIn 4.49 h 336 (5.1±0.7) 10-3 15.065

114Sn (, p) 113mIn 1.66 h 392 (8.8 ±1.0)10-3 14.32

176Yb 174Yb (, p) 173Tm 8.24 h 399 (0.75±0.15)10–3 15.72

natHf 178Hf (, p) 177gLu 6.65 d 208 (1.8±0.4)10–3 15.33

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RELATIVE YIELDS OF (RELATIVE YIELDS OF (, , pp) AND () AND (, , ) IN RATIO TO () IN RATIO TO (, , nn) REACTIONS ) REACTIONS AT AT EEee=23 MEV VERSUS THRESHOLD PARAMETER VALUE. =23 MEV VERSUS THRESHOLD PARAMETER VALUE.

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Z–DEPENDENCE OF THE (Z–DEPENDENCE OF THE (, , ) - REACTION YIELD. ) - REACTION YIELD. SOLID CURVE GIVES THE GUIDE FOR EYES.SOLID CURVE GIVES THE GUIDE FOR EYES.

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REACTION MECHANISM PATTERNREACTION MECHANISM PATTERN 11

• At low energy, (, ) yield is suppressed, probably, due to the pre-formation factor same as in decay;

• With 100 MeV protons, electrons, and photons, the pre-equilibrium exiton model is applicable:

J.R.Wu and C.C.Chang, Phys.Rev., C17, 1540 (1978) – theory.

• Formation factor for of about (10-2 – 10-3) is deduced from experiments.

W.R.Dodge, et.al., Phys.Rev., C32, 781 (1985):

- yield by 20 times lower the proton emission;

• This model is hardly applicable to the case of 23 MeV bremsstrahlung.

Free energy of about 5-7 MeV above threshold does not allow generation of 4 excitons by photons;

• Conclusion: preformation factor as in decay is preferable.

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REACTION MECHANISM PATTERNREACTION MECHANISM PATTERN 22

1. Alpha-emission must be suppressed when no quasi-free α is available in a nucleus, but at the same time nucleons are ready for ejection;

2. Nucleons within the unexcited target nucleus are located and paired at definite orbits. They manifest themselves as non-interacting particles due to the Pauli principle;

3. In reactions with charged particles (HI), a strong impact of the projectile generates immediately a directed flow of perturbed nucleons and they could easily be joined together forming an α-cluster due to “Internal coalescence”.

HI

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SCHEME OF INNA PROCESS WITH THERMAL NEUTRONSSCHEME OF INNA PROCESS WITH THERMAL NEUTRONS

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INNA TRANSITIONS WITH INNA TRANSITIONS WITH 178m2178m2Hf AND Hf AND 180m180mTaTa

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CROSS SECTION OF THE INNA PROCESSCROSS SECTION OF THE INNA PROCESS (S(S00 is ht S wave strength function) is ht S wave strength function)

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TRANSMISSION COEFFICIENTS TTRANSMISSION COEFFICIENTS Tℓℓj j FOR NEUTRONS FOR NEUTRONS

WITH ORBITAL MOMENTUM WITH ORBITAL MOMENTUM ℓℓ ( (178178Lu NUCLEUS)Lu NUCLEUS)

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SINGLE PARTICLE LEVELS OF SHELLSINGLE PARTICLE LEVELS OF SHELL

Internal orbital momentum of nucleons is great, like 5,6,7.

N=107 (180Ta)

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SUMMARY: MODIFICATION OF MECHANISMSUMMARY: MODIFICATION OF MECHANISM

Centrifugal barrier allows emission of neutrons with minimum orbital momentum ℓ=0;1;2.

Neutrons sitting at ℓ=3-7 orbits must proceed through the re-arrangement of orbital moments. So that, emission rate is suppressed and statistical decay widths are reduced.

Possible process is virtual tunneling of a neutron pair with ℓ=0 and consequent pair break outside of the nucleus. One of neutrons remains inside nucleus and another one is emitted with high ℓ.