“Study of light nuclei interactions in the astrophysical energy region" (Project “LESI”) V.M. Bystritsky Collaboration: JINR – INP TPU (Tomsk, Russia) – HCEI RAS (Tomsk, Russia) – LPI RAS (Moscow, Russia) – UCI (Irvine, USA) – FPACS AGH (Krakow, Poland) – IEE SAS (Bratislava, Slovakia) – FFE AGH (Krakow, Poland) – INP NNC (Almaty, Kazakhstan)

Motivation verifying the charge symmetry in strong interactions at ultralow energies obtaining information on exchange meson currents verifying correctness of few-body systems description on the basis of modern concepts of nuclear interaction between constituent nucleons obtaining information on the size of electron screening of interacting nuclei to explain on existing deficit of light nuclei (except 4 He) in stars and the Galaxy to test applicability of the standard model to the description of all processes occurring in the Sun

Aim of the research Measurement of astrophysical S-factors, effective cross sections and potential of electron screening for pd, dd, d 3 He and reactions in the ultralow energy region (2-15 keV) Bottlenecks nuclear reaction cross sections for such energy region (2-15 keV) are very small σ ≈ cm 2 intensities of accelerated p, d, 3 He beams using classical accelerators are too low

SGM HCEI I ≈ 950 кA, τ = 80 ns Institute of high-current electronic RAS (Tomsk, Russia) plasma accelerators MIG I ≥ 1.7 MA, τ = 80 ns

Conclusion on Z pinch data Problems with Z-pinch The dd and pd results obtained for the first time with the help of plasma accelerators indicate that, on the one hand, the proposed technique is worthy and can be used to study nuclear reactions in the astrophysical energy region On the second hand the pulsed power Z-pinch technology cannot provide the required accuracy of the measured characteristics due to its single-pulse operation mode, and respective low shot-to-shot reproducibility of experimental conditions To alleviate the named drawbacks for the generation of H +, D + and 3 He + ions flows in the energy range 2-15 keV we designed and built a modified pulsed Hall accelerator (HA)

Plasma Hall accelerator Plasma Hall accelerator 1 – anode holder, 2 – insulator, 3 – shock coil, 4 – Laval nozzle, 5 – pulse gas valve, 6 – first-step anode, 7 – second-step anode, 8 – conic cathodes, 9 – electromagnet, 10 – Rogovsky belt B = 1.6 kGs in the middle of the ring gap average diameter of the second anode – 170 mm square of emitted surface – 95 cm2 voltage of shock coil – 20 kV duration of plasma pulse – 1÷50 μs rise time of plasma pulse – 200 ns amplitude unstability in the high voltage pulse – 0.5 % current – 200 A generator of accelerated voltage – 2÷20 kV

Pulse Hall Accelerator Hall plasma source uses an electrodeless induction discharge with pulsed gas bleed-in The fundamental feature of HA is the acceleration of ions in a magnetized plasma channel across the externally applied B-field plasma density is – (1 ‑ 2)  cm -3, which corresponds to the ion saturation current ~ (1-3) A/cm 2 Conclusion: Hall ion source is very effective for high intensity plasma flux formation

Experimental determination of the astrophysical S-factor and effective cross section of the dd, pd and d 3 He reactions: – yield of the detected particles (i = n, γ, α), N p – number of particles hit in the target (p = p, d, 3 He), Z 1, Z 2 and  – charges and reduced mass of the colliding particles, n t – density of the target,  γ – efficiency of the reaction products detection, E kd – energy of colliding particles in c.m. after passage of a target layer of thickness x, Ē kd – average energy of the of colliding particles, f(E kd ) – energy distribution of the particles hitting the target, – effective target thickness defined from the expression ( – yield of products from the dd, pd and d 3 He reaction in the case of an the infinitely thick target). Measurement method

Electron Screening in the fusion reactions R D – electron Debye radius arround the deutrons T – temperature of the free electrons in inits K N eff – number of valence electrons per metallic atom ρ a – atomic density, at/cm 3 There is a theoretical assumption that during star evolution process with high density of star substance the increase of the nuclear reaction rates caused by electron screening of interacting nuclei. The effect becomes significant when the density of substance became  g/cm 3 – a case of strong screening effect.

Targets (1) vacuum measuring chamber, (2) flask containing heavy water, (3) valve, (4) nozzle, (5) D 2 O target, (6) copper disk, (7) central collimation hole, (8) electrostatic multigrid spectrometer, (9) collector, (10) copper cold finger, (11) dewar liquid nitrogen. (1) chamber, (2) driver, (3) magnetic clutch, (4) rotating cylinder, (5) film for metal sputtering, (6) magnetron, (7) sputtering metal. Target: Ø97 mm, d=2 mm copper substratum, thickness of deuterated layer 3 μm Cryogenic D 2 O targetMetallic targets (magnetron sputtering method)

Diagnostics equipment Electrostatic multigrid spectrometer of charge particles for Electrostatic multigrid spectrometer of charge particles for measurement of energy distribution of ions generated by the Hall accelerator Collimated Faraday cup arrays for current density measurement in various ion beam sections Rogowski belt for measurement of Ion current Double and face probes located along the axis of the plasma gun for measurement of plasma density of the deuterium (hydrogen) concentrationdistribution in the metallic targets ( Method of elastic recoil detection (ERD) and Rutherford back scattering for measurement of the deuterium (hydrogen) concentration distribution in the metallic targets (Van de Graaf accelerator) Method of Auger Spectroscopy for determination of the target surface layer composition

Experimental setup for measuring of deuteron concentration distribution

Study of the dd-reaction in the astrophysical energy region using the plasma Hall accelerator with using the D 2 O, CD 2 and ZrD 2 targets 1) deuterium target (CD 2, D 2 O, ZrD 2 ); 2) electrostatic multigrid spectrometer; 3) plastic neutron detectors (480×100×100 mm); 4) rogovsky belt; 5) small-size collector (Faraday cup).

dd experimental results Potentials of electron screening for dd reaction in D 2 O, CD 2 and ZrD 2 targets are obtained: U e (D 2 O) < 22 eV; U e (ZrD 2 )< 30 eV (U e (D 2 ) = (25±5) eV [U. Greife et al., Z. Phys. A 351, (1995) ]; U e (ZrD 2 )= (297±8) eV – [K.Czerski et al., Eur. Phys.. Lett. 54 (2001) 449 ])

Conclusion on the dd experiment First of all we have received the data on S-factor and cross section of dd → 3 He + n reaction in the collision energy range ( keV) with using of the CD 2,, D 2 O and ZrD 2 targets There is no difference within the range of errors between our data obtained with CD 2, D 2 O and ZrD 2 targets using Z pinch technology and Hall accelerator in the deuteron collision energy range keV There is a substantial difference between our data and data measured in the other experiments with metal targets Zr, Ta, Al, Hf saturated by deuterium For receiving the answer – Is there an experimentally noticeable intensity enhancement effect in dd-reaction caused by electron screening? – it is necessary to use metallic targets (Ta, Zr, Pt, Hf, Pd, Mo…) with high density of quasi-free electrons saturated by deuterium

pd experimental results Three runs with the D 2 O target were carried out and average values of the S pd factor and cross-section of the pd reaction were found: S pd (E col =8.28)=(2.37±0.71)·10 −4 keV·b, S pd (E col =9.49)=(2.77±0.64)·10 −4 keV·b, S pd (E col =10.10)=(2.98±0.65)·10 −4 keV·b Our first results and the discrepancy between results existing in the literature for sure stimulate the continuation of pd reaction study to get more detailed information on this process in the ultra-low energy (the cause of such discrepancy still remains unclear)

Study of the d 3 He-reaction in the astrophysical energy region using the plasma Hall accelerator Conclusion There is the substantial difference between results obtained in [Aliott – Nucl. Phys. A690 (2001) 790; Prati – Z. Phys. A350 (1994) 171; Engstler – Phys. Let. B202 (1988) 179; Geist – Phys. Rev. C60 (1999) ]. The screening potentials differ due to the molecular and atomic aggregate state od the targets and significantly larger then expected from avaible atomic physics model. Dependence of S-factor for 3 He(d, p) 4 He reaction from energy collision of nuclei 3 He with deuterons. Solid line – result of the fit with of electron screening potential of 219 eV; dotted line – result of calculation for interaction of bare nuclei 3 He and deuterons

Period : Modernization of the Hall accelerator: the total amount of the accelerated deuterons, protons and 3 He ions in the energy region of 3-15 keV will be increased up to the level ions per pulse; pulse repetition rate of ~1 Hz Extending the experimental possibilities of the setup: creating the silicon detectors for registration of the charged particle products (p, α) from dd, d 3 He reactions Measuring with high accuracy the astrophysical S factors and effective cross sections of the dd, pd and d 3 He reactions in energy region 2-15 keV with using the Hall accelerator and targets from TiD 2,TaD, ZrD 2, D 2 O and CD 2 Quantitative determination of the influence of the electron screening effect on the increase of the dd-, d 3 He reaction cross-sections with decreasing of the collision energy using the targets from TiD 2,TaD, ZrD 2. For the d 3 He reaction this information will be obtained for the first time Plans

Statistics Reaction Valued + d → 3 He + n d + d → t + n d + p → 3 He + n d + 3 He → p + α Collision energy region, keV 1.3 ≤ E col ≤ ≤ E col ≤ ≤ E col ≤ 6.0 Target TiD 2, TaD, ZrD 2, D 2 O Time of statistics collection, day Determinable magnitudes S dd (E col ) = f(E col ) U e dd ; σ dd eff (E col ); S pd (E col )=f(E col ); U e pd ; σ pd eff (E col ); S d3He (E col )= f(E col ); U e d3He ; σ d3He eff (E col ) In comparison with using of the classical accelerators we will spend for statistics collection in 80 times less.

List of main publications in refereed journals ( ) 1.Neutron Emission at the collision of plasma opposing fluxes in the external magnetic field, Plasma Physics, 31 (2005) Study of the pd reaction at ultralow energies using hydrogen liner plasma, Physics of Atomic Nuclei, 68 (2005) Scintillation detectors in the experiments on the plasma accelerators, Pribory and Techn. Exper., 6 (2005) Application of inverse Z-pinch for study of the pd reaction at keV energy range, Nucl. Instr. Methods (2006) Investigation of the input energy processes in the region of plasma fluxes collision with opposite on direction fields of polarization, Letters to Journal of Technical Physics, Letters to Zh. Tekh. Fiz. 33 (2007) Study of the d(d,n) 3He reaction in the astrophysical energy region with the use of the Hall accelerator, Eur. Phys. J. A36 (2008) Study of the pd-reaction in the astrophysical energy region using using the Hall accelerator, Nuclear Instrum. Meth. A595 (2008)