Resonance Conversion as a Catalyser of Nuclear Reactions
aa r X i v : . [ nu c l - t h ] A ug Resonance Conversion as a Catalyser of NuclearReactions ∗ KARPESHIN Feodor , , ZHANG Jingbo , and ZHANG Weining Science Center and Department of Physics, Harbin Institute of Technology, Harbin 150001 Fock Institute of Physics, St. Petersburg State University, RU-198504 St. Petersburg, Russia
It is shown that resonance interal conversion offers a feasible tool for mastering nuclear processes with laseror synchrotron radiation. Physics of the process is discussed in detail in historical asprct. Possible wayof experimental applicaytion is shown in the case of the M Yb. Nu-clear transition rate in hydrogenlike ions of this nuclide can be enhanced by up to four orders of magnitude.PACS: 23.20.Nx, 42.65.-k, 42.62.-b
In 1939, Bohr and Wheeler proposed the version ofnuclear theory, which since that time is applied for de-scription of this wonderful process [1]. Ten years later,Wheeler told out an idea that fission of
U nucleusin the muonic atom can be induced by a radiation-less muon transition 2 s → s [2]. Later investigationshowed that the population of the 2 s level is less prob-able, of a few percent of that for the 2 p state, andadditionally, the radiative 2 s → p transition makes astrong competition. However, it was shown that theradiationless transition probability for higher multi-poles, E p, p → s transition[3], E d → s [4,5], and even E d → p transi-tion[6,7] are all of approximately the same probability.Experiments fully confirmed the Wheeler’s conjectureand the further predictions[8].In ref.[6,7] special attention was brought to the factthat the radiationless transition is a reverse conversionprocess. It was considered in terms of the radiative nu-clear width and internal conversion coefficients(ICC).That explained the reason why higher multipole tran-sitions turn out to be of about the same probabil-ity. In 1958, Morita proposed a similar process ofNuclear Excitation in Electron Transition, which issince known as NEET[9]. Calculations[6,7] revealedthe strong resonance coupling arising in atoms betweenthe nucleus and the shell, or the muon in the caseof muonic atom. This coupling offers a real tool ofmastering nuclear electromagnetic transitions throughresonance with the electron shell, using laser or syn-chrotron radiation.The present paper is built as follows. (i)We remindin main features general internal conversion(IC) the- ∗ Supported by Russian Foundation for Basic Research(05-02-17340) and Scientific Research Foundation of Harbin Instituteof Technology (HIT.2003.23) ory. (ii)We present the theory of the resonance internalconversion and outline experiments where it was dis-covered. (iii)We propose a way of mastering the rateof the resonance conversion by applying external laseror synchrotron radiation, and consider concrete exam-ples.
As a result of prompt fission, the muon is entrained onone of the fragments, mostly on the heavy one. Thefragment is excited, and emits γ ′ s , neutrons, protons,alphas. Emitted γ ′ s can be absorbed by the muon,which leaves the atom (Fig.1). Such a process is well Fig.1.
Feynman graph of internal conversion. known in electronic atoms. It is called internal con-version (IC). The necessary condition is ω n > I (1)where ω is the nuclear transition energy and I is theionization potential.A very useful value is ICC, which is defined as theratio of the conversion and radiative transition proba-bilities, α ( τ L ) = Γ c Γ ( n ) γ , (2)1 , L being the type and multipole order of the tran-sition. α is nearly independent of the nuclear model.This allows one to reverse eq.(2) and put downΓ c = α Γ ( n ) γ . (3)Values of α are tabulated. Eq. (3) hence allows one toestimate the conversion transition probability, as soonas the radiative nuclear width is known. IC is one ofthe principal tools for nuclear spectroscopy. If condition (2) is broken, i.e. ω n < I , the conversionelectron cannot leave the atom. It occupies an ex-cited electron level, forming an unstable intermediatestate (Fig.2). This state then undergoes decay. This is Fig.2.
Feynman graph of the resonance internal conversion. mainly performed by the radiative electron transition,filling the hole formed in the place of the conversionelectron. We still can formally calculate the α valueby means of the formula, used for the traditional ICCcalculations, inserting the wave function of the relateddiscrete atomic state as the conversion electron func-tion: α d ( τ L ) = X κ | M ( τL ) κ | , M ( τL ) κ = Q ( L ) κ R ( τL ) κ (4) Q ( L ) κ = − r απωL ( L + 1) C j f − j i − L ; R ( ML ) κ = ( κ + κ )( R + R ) R ( EL ) κ = L ( R + R ) + ( κ i − κ f − L ) R ++( κ i − κ f + L ) R with R i — the radial integrals R = Z ∞ G i F f X L dr R = Z ∞ F i G f X L drR = Z ∞ F i F f X L dr R = Z ∞ G i G f X L drR = Z ∞ G i F f X L − dr R = Z ∞ F i G f X L − dr. Here α d ( τ L ) is the discrete ICC, τ L is the type andmultipole order of the transition, EL and M L standfor the electric and for the magnetic types, respec-tively. Subscripts i and f denote the initial and finalstates, respectively; κ = ( l − j )(2 j + 1) is the rela-tivistic quantum number, with l , j for the orbital andtotal angular moments; G and F are the big and smallcomponents of the radial wave function, normalized at Z ∞ [ G + F ( r )] dr = 1 . (5)Furthermore, α ≈ M ( τL ) κ are the conversion matrix elements, ω is the nu-clear transition energy. R − are the radial integrals,with X ν the interaction potential of the nuclear andelectron transition current. With account of the finitenuclear size, the latter becomes X ν = h ν ( ωr ) (6)for r ≥ R , with R — the nuclear radius. For r < R ,nuclear model of the surface transition current pro-vides an adequate description[10]: X ν = h ν ( ωR ) j ν ( ωR ) j ν ( ωr ) . (7)In the case of discrete conversion, however, the α d value acquires dimension of energy, due to anothernormalization of the wavefunction[11]. Therefore, itcannot serve as ICC (2) anymore. There is an evidentway, to form a dimensionless factor R by multiplying α d by the resonance Breit-Wigner factor. We add asubscript d to the sign of α d , to distinguish it from atraditional ICC. Then the expression for R becomesas follows: R = α d Γ / π ∆ + (Γ / , (8)where Γ is the full width of the intermediate atomicstate, and ∆ is the defect of the resonance of the nu-clear and electron transitions. With the account ofBIC, resulting lifetime of the nuclear level will be λ = λ γ α tot + R , where λ γ is the radiative lifetime, and α tot is the totalICC. It follows from eq.(4) that the BIC probability can beenhanced in the case of resonance by the value of R res R ≃ (cid:18) ∆Γ (cid:19) . (9)2or nuclei, typical values of ∆ ≃ ∼
20 eV (which is a typical K -hole width), or ∼ − –10 − eV in the case of BIC in the outer elec-tron shells. Therefore, expected effect can be aroundten orders of magnitude and more [12, 13].The idea is to arrange a two-photon resonance.Consider atom in an external field of a plane electro-magnetic wave. Some atomic electron can go to anexcited state by absorption of one or several photonsfrom the field. The probability of multiphoton ab-sorption increases drastically if the total energy of theabsorbed photons approaches the difference of the elec-tron levels. This effect is used by RIS — resonance ion-ization spectroscopy. Let us consider the two-photonresonance, and replace one photon of the field by thenuclear photon [15]. This is laser assisted nuclear BICtransition, as the electron makes a two-photon tran-sition to an excited state, one photon being from thenucleus, and the other from the field. Necessary con-dition is then ω n ± ω l = ω a . (10)The two signs in (6) correspond to either an absorp-tion, or induced emission of a photon of the field. Theboth probabilities are of the same value. Typical nuclear sizes are of the order of R ≃
10 Fm.Typical scale for their transition energies is of ∼ ǫ ≃ V /cm . At such strength,spontaneous generation of e + e − pairs already takesplace (Klein’s paradox[16]). Such a simple estimatehelps to realize that all the photo-nuclear reactionsare due to resonance effect. Only resonance quantacan be absorbed by the nuclei, with the energy whichexactly equals the nuclear level separation energy.Another lesson is why the only isomer was probablytriggered up to now, that of Ta, in spite of tremen-dous experimental efforts applied in this field[13].Finally, atomic size is by four orders of magnitudelarger than the nuclear one. This means that it ismuch easier to affect the nucleus by electromagneticfield through mediation of the electron shell, whichplays a role of resonator[15]. In view of the above-mentioned difficulties related with triggering the iso-mers, one must not afford a neglecting of several ordersof magnitude gain which can be benefited from makinguse of the resonance properties of BIC. Further experi-mental study in the field must be directed in this way.We show in a separate paper a concrete example of this idea as applied to the
Hf isomer.
A bright example of resonance effect of BIC is providedby characteristic muonic X-rays from heavy promptfission fragments. This radiation arises due to reso-nance excitation of the bound muon to the 2 p state,with reemission in the succeding back muon transition2 p → s . This resonance effect predicted in ref.[10] isshown in Fig.3. The effect was experimentally studied Fig.3.
Spectrum of γ rays from prompt fission fragments, cal-culated with the account of the µ in the orbit. in paper[15]. It was shown that taking this processinto account leads to better value of χ in filling theexperimental spectrum of γ rays from prompt fissionfragments.The other example was demonstrated by the 35-keV M Te[13]. In neutral atom, thislevel mainly deexcites via IC in the K shell, with α ( M
1) = 11 .
5. But for 45- and 46-fold ions the con-dition (1) is broken. It was therefore expected thatthe lifetime will increase for these ions by an orderof magnitude (Fig. 4). Experiments however showedthat the lifetime holds[13]. The observed paradox wasexplained by the resonance conversion — BIC, whichtakes place of the ordinary one. In the succeding pa-pers, the fluorescence yield from the 1 s -hole statescaused by the resonance conversion was observed. Theobserved numerical probability of BIC came to accor-dance with theory.
A very promising experiment can be undertaken inhydrogen-like ions of
Yb. The energy of the M s → s transition. Therefore,3 ig.4. Scheme illustrating how traditional internal conversiontransforms into the resonance one in ionized atoms of
Te. it is expected that the nuclear lifetime shall be consid-erably shortened in the field of electromagnetic waveof such frequency[18]. This effect is demonstrated inFig.5. As one can see, the effect can achieve up to fouroders of magnitude.A very promising field of application of the reso-nance BIC is the laser produced plasma. Then NEET,which is a reverse BIC process, is one of the possi-ble mechanisms which can lead to formation of nu-clear isomers in a heat bath[19, 20]. This mecha-nism is under experimental investigation at the timebeing, specifically, with respect to the 76-eV
Uisomer[21], 1.5-keV
Hg isomer[22], 6-keV
Ta iso-mer [23], and others. Further peculiarities of NEETarising in plasma are considered in paper[24].Some of the results presented above were deliveredon the conference [25] held under honorary patronageof J. Wheeler. He was satisfied to know about devel-opment of his idea.
Fig. 5.
Values of the resonance enhancement factor R calcu-lated for the hydrogenlike ions of Yb versus intensity of theexternal field.
References [1] Bohr N and Wheeler J A 1939 Phys Rev
426 [2] Wheeler J A 1948 Phys Rev G17
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JETP 2004 B372 C70044303[22] Meot 2005 Invited talk at the AFOSR Workshop “Laser-05Dibna[23] Andreev A 2005 Invited talk at the AFOSR Workshop“Laser-05” JINR Dubna[24] Karpeshin F F in Applications of Lasers in Atomic NucleiResearch Proceedings of the V International Workshop on“Prospects for the development of Laser Methods in theStudy of Nuclear Matter” May 28-31 2001 Poznan PolandDubna 2002 P176.[25] Fission Dynamics of Atomic Clusters and Nuclei Proc ofthe Int Workshop FDACN-2000 Luso Portugal 15-19 May2000 Ed J da Providencia Brink D M Karpechine F andMalik F B Singapore World Scientific 2001