Measured Momentum Distributions Research Articles

Dose estimation using in-beam positron emission tomography: Demonstration for 11C and 15O ion beams

Ion therapy has been well established for many decades owing to sharp depth-dose gradient and high cell-killing capability of ions. However, monitoring of the incident ions is needed to reduce ion range uncertainty for effective tumor treatment. Positron-emitting ion beams, known as radioactive ion (RI) beams, can be used as the optimal clinical approach for simultaneously treating and monitoring the incident ions using positron emission tomography (PET) imaging. The low intensity of RI beams, which previously was the main difficulty of their clinical use, was recently addressed by the development of accelerator technology. Since the quantity of interest in ion therapy is the dose and a direct comparison of planned and delivered doses is highly desirable, we focused on predicting the depth dose from PET images for RI beams in this work for the first time. We developed a method for predicting the depth dose of polyenergetic ion beams of 11C and 15O from PET images of these ion beams. The depth dose in water was measured for mono- and polyenergetic ion beams. The monoenergetic ion beams had a momentum acceptance (MA) of ±0.25%, while the polyenergetic beams had an MA of ±2.5%. PET imaging was performed during and shortly after irradiation of a polymethylmethacrylate (PMMA) phantom with mono- and polyenergetic radioactive ion beams. The energy distribution of each polyenergetic ion beam was obtained from the measured momentum distribution of that beam. A set of depth dose and PET profiles in PMMA was constructed for several monoenergetic ion beams using measured data of a monoenergetic ion beam and the range-energy relation. To estimate the depth dose for each polyenergetic beam, a linear combination of weighted PET profiles of monoenergetic beams was iteratively fitted to the measured PET profile of the polyenergetic beam, and the resulting weights were combined with the corresponding monoenergetic depth doses to predict the depth dose distribution. Significance. The depth doses of the polyenergetic ion beams were predicted with mean relative errors of 2.20% and 1.95% for 11C and 15O ion beams, respectively. These errors represent the mean value of the differences between the predicted and measured values, normalized to the maximum measured value. The predicted distal fall-off positions at 80% of the Bragg peak were within 0.13 mm of the measured values for both ion beams. The applicability of the method was demonstrated for a head phantom irradiated with 11C ion beams using Monte Carlo simulation and the predicted distal fall-off positions at 80% of the Bragg peak was within 0.08 mm of the simulated values.

Advances in a measurement method of rainfall kinetic power and momentum affecting soil erosion processes

AbstractRainfall is one of the factors affecting soil erosion, and rainfall kinetic energy or momentum is used to represent the capability of the precipitation to erode soil, named rainfall erosivity. Accurate measurements of rainfall erosivity are useful for a reliable prediction of soil loss. Rainfall momentum and kinetic energy, both calculated per unit time and area, can be obtained using terminal raindrop velocity and the drop size distribution (DSD) measured by disdrometers, which are instruments expensive and not suitable for large scale use. An innovative patented method to measure the rainfall energy is based on the estimation of DSD by simultaneous detection, in a given time interval, of the rainfall intensity I and the number N of raindrops that hit a specific piezoelectric surface. In this paper, advances of this method are presented. In particular, two new theoretical procedures to estimate the parameters μ and Λ of Ulbrich's distribution, that allow for the calculation of the rainfall kinetic energy and momentum, are proposed. Both procedures (Scenario 1 and 2) are based on the frequency distribution of the momentum M(D) of raindrops detected in a sampling time interval. Specifically, in the Scenario 1, μ and Λ are estimated by using I, N and the standard deviation, s(D), of the drop diameters obtained from the measured momentum distribution. In the Scenario 2 the parameters are estimated using I, N and the mean value, m(D), of the drop diameters deriving from the momentum distribution. The reliability of the proposed procedures was tested using DSD measurements recorded in three different experimental sites. The developed analysis demonstrated that Scenario 2 is the best method to estimate μ and Λ, and to reproduce the DSD, accordingly. The proposed method, associated with a patented device, not yet build, will allow the direct measurement of the rainfall energy characteristics, which are usually roughly estimated from rainfall intensity. The possibility to easily measure these energy variables can support the development of research in the field of soil erosion and, in general, of hydrogeological instability. In particular, the proposed measurement method and the construction of the device could stimulate the scientific community to deepen the study of the effect of the rainfall energy on soil erosion for improving the predictive capability of water erosion models.

H6 states studied in the H2(He8,He4) reaction and evidence of an extremely correlated character of the H5 ground state

The extremely neutron-rich system $^{6}$H was studied in the direct $^2\text{H}(^8\text{He},{^4\text{He}})^{6}$H transfer reaction with a $26 A$ MeV secondary $^{8}$He beam. The measured missing mass spectrum shows a broad bump at $\sim 4-8$ MeV above the $^3$H+$3n$ decay threshold. This bump can be interpreted as a broad resonant state in $^{6}$H at $6.8(5)$ MeV. The population cross section of such a presumably $p$-wave state (or may be few overlapping states) in the energy range from 4 to 8 MeV is $d\sigma/d\Omega_{\text{c.m.}} \simeq 190^{+40}_{-80}$ $\mu$b/sr in the angular range $5^{\circ}<\theta_{\text{c.m.}}<16^{\circ}$. The obtained missing mass spectrum is practically free of the $^{6}$H events below 3.5 MeV ($d\sigma/d\Omega_{\text{c.m.}} \lesssim 5$ $\mu$b/sr in the same angular range). The steep rise of the $^{6}$H missing mass spectrum at $\sim 3$ MeV allows to derive the lower limit for the possible resonant-state energy in $^{6}$H to be $4.5(3)$ MeV. According to the paring energy estimates, such a $4.5(3)$ MeV resonance is a realistic candidate for the $^{6}$H ground state (g.s.). The obtained results confirm that the decay mechanism of the $^{7}$H g.s.\ (located at 2.2 MeV above the $^{3}$H+$4n$ threshold) is the "true" (or simultaneous) $4n$ emission. The resonance energy profiles and the momentum distributions of fragments of the sequential $^{6}$H$ \,\rightarrow \, ^5$H(g.s.)+$n\, \rightarrow \, ^3$H+$3n$ decay were analyzed by the theoretically-updated direct four-body-decay and sequential-emission mechanisms. The measured momentum distributions of the $^{3}$H fragments in the $^{6}$H rest frame indicate very strong "dineutron-type" correlations in the $^{5}$H ground state decay.

Positron pair interactions in a nearly free-electron metal

The electric field surrounding a single positron in a metal is screened by an increase in the local electron density which, in the case of nearly free-electron metals (like Al, Na, etc.), has a radial distribution similar to that of the electron in positronium (Ps). In such metals, a singlet pair of positrons would experience an attractive interaction and at low enough electron densities could possibly form a bound state that is held together by exchange and correlation energies, thus forming structures analogous to that of the positronium molecule (Ps_2), with binding energies of a few tenths of an eV. Such di-positrons could be prevalent at positron densities of around 10^{18} cm^{-3} and, if so, would be evident from an apparent broadening of the sharp step at the Fermi surface in measurements of the electron momentum distribution by the angular correlation of the 2gamma annihilation radiation. Even if di-positrons are not directly formed in a metal, optical spectroscopy of Ps_2 formed in vacuum via pairs of positrons simultaneously being emitted from the surface could be applied to the direct measurement of the momentum distribution of Cooper pairs. If they exist, di-positrons in metals would yield interesting information about electron and positron interactions and at very high densities might allow the study of a di-positron Bose–Einstein condensate immersed in an electron gas.Graphic

Clusters and their fundamental role for Trojan Horse Method

The Trojan Horse Method (THM) lays its foundations on the cluster structure of light nuclei which are usually used as “Trojan horses”. Many of them were successfully employed in the last decades to shed light to numerous astrophysical problems. Cluster structure and dynamics also suggest a series of tests which may be performed in order to strengthen the basis of the method. Among them pole invariance was investigated for three different situations. In fact, the cross sections for the $$^6$$ Li(d, $$\alpha )^4$$ He, $$^2$$ H(d,p) $$^3$$ H and $$^7$$ Li(p, $$\alpha )^4$$ He binary reactions were measured for several break-up schemes and analyzed within the framework of the Plane Wave Impulse Approximation (PWIA). The indirect results extracted by using different Trojan Horse nuclei (e.g. $$^2$$ H, $$^3$$ He, $$^6$$ Li) were compared with each other as well as with direct measurements of the corresponding astrophysical reactions. The very good agreement obtained confirms the applicability of the pole approximation and of the pole invariance method, namely the independence of binary indirect cross section on the chosen Trojan Horse nucleus, at least for the cases investigated. Moreover, we can verify that the effect of using a charged or a neutral particle as a spectator implies negligible corrections consistent with the experimental errors. In addition, the dynamics of clusters inside the Trojan Horse nucleus and their fingerprints on the measured momentum distribution play a key role for THM applications. In this article we will therefore discuss also these assertions studied in different systems( $$^2$$ H, $$^3$$ He, $$^6$$ Li, $$^9$$ Be, $$^{14}$$ N) and in particular for the deuteron case the relative impact of s and d waves in the momentum distribution will also be examined.

Ellipticity-dependent sequential over-barrier ionization of cold rubidium

We perform high-resolution measurements of momentum distribution on Rb$^{n+}$ recoil ions up to charge state $n=4$, where laser-cooled rubidium atoms are ionized by femtosecond elliptically polarized lasers with the pulse duration of 35 fs and the intensity of 3.3$\times$10$^{15}$ W/cm$^2$ in the over-barrier ionization (OBI) regime. The momentum distributions of the recoil ions are found to exhibit multi-band structures as the ellipticity varies from the linear to circular polarizations. The origin of these band structures can be explained quantitatively by the classical OBI model and dedicated classical trajectory Monte Carlo simulations with Heisenberg potential. Specifically, with back analysis of the classical trajectories, we reveal the ionization time and the OBI geometry of the sequentially released electrons, disentangling the mechanisms behind the tilted angle of the band structures. These results indicate that the classical treatment can describe the strong-field multiple ionization processes of alkali atoms.

In situ momentum-distribution measurement of a quantum degenerate Fermi gas using Raman spectroscopy

The ability to directly measure the momentum distribution of quantum gases is both unique to these systems and pivotal in extracting many other important observables. Here we use Raman transitions to measure the momentum distribution of a weakly-interacting Fermi gas in a harmonic trap. For narrow atomic dispersions, momentum and energy conservation imply a linear relation between the two-photon detuning and the atomic momentum. We detect the number of atoms transferred by the Raman beams using sensitive fluorescence detection in a magneto-optical trap. We employ this technique to a degenerate weakly-interacting Fermi gas at different temperatures. The measured momentum distributions match theoretical curves over two decades, and the extracted temperatures are in very good agreement with the ones obtained from a conventional time-of-flight technique. The main advantages of our measurement scheme are that it can be spatially selective and applied to a trapped gas, it can be completed in a relatively short time, and due to its high sensitivity, it can be used with very small clouds.

A combined deep inelastic neutron scattering and ab initio lattice dynamics study of the hydride anion dynamics and bonding in La2LiHO3 oxyhydride

Kobayashi et al (6279) (Science 2016, 351) reported recently the existence of pure H- conductivity in the oxyhydride La2−x−ySrx+yLiH1−x+yO3−y, while demonstrating its functionality through a prototype solid-state Ti/La2LiHO3/TiH2 battery. In this study, we probe the atomistic motion of La2LiHO3 obtained by the promising halide salt flux method, via a combination of deep inelastic neutron scattering (DINS) and ab initio lattice dynamics (LD) calculations verified by vibrational inelastic neutron spectroscopy (INS). We successfully describe the measured momentum distributions from DINS via our LD calculations, without observing any diffusion activation over the temperature range reported by Kobayashi et al. This observation is corroborated by model predictions from our LD study, which reveals that the hydride anions remain bound within a 3D-harmonic potential. We conclude that with the current synthesis parameters, the method produces a vacancy free lattice, and that a necessary ingredient for diffusive motion of H- is the presence of a large population of vacancies. Based on the harmonic prediction for the hydrogen kinetic energy, we derive a picture of the evolution of the effective bonding potential for the hydride anions, and link this to the dynamics associated with decomposition of the oxyhydride.

Modeling quantum yield, emittance, and surface roughness effects from metallic photocathodes

Detailed measurements of momentum distributions of emitted electrons have allowed the investigation of the thermal limit of the transverse emittance from metal photocathodes. Furthermore, recent developments in material design and growth have resulted in photocathodes that can deliver high quantum efficiency and are sufficiently robust to use in high electric field gradient photoinjectors and free electron lasers. The growth process usually produces photoemissive material layers with rough surface profiles that lead to transverse accelerating fields and possible work function variations, resulting in emittance growth. To better understand the effects of temperature, density of states, and surface roughness on the properties of emitted electrons, we have developed realistic three-dimensional models for photocathode materials with grated surface structures. They include general modeling of electron excitation due to photon absorption, charge transport, and emission from flat and rough metallic surfaces. The models also include image charge and field enhancement effects. We report results from simulations with flat and rough surfaces to investigate how electron scattering, controlled roughness, work function variation, and field enhancement affect emission properties. Comparison of simulation results with measurements of the quantum yield and transverse emittance from flat Sb emission surfaces shows the importance of including efficient modeling of photon absorption, temperature effects, and the material density of states to achieve agreement with the experimental data.

Quantum criticality and the Tomonaga-Luttinger liquid in one-dimensional Bose gases.

We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributions of the 1D ultracold gas, confirming the existence of the TLL.

Kinetic energy and momentum distribution of isotopic liquid helium mixtures.

The momentum distribution and atomic kinetic energy of the two isotopes of helium in a liquid mixture at temperature T = 2 K are computed by quantum Monte Carlo simulations. Quantum statistics is fully included for 4He, whereas 3He atoms are treated as distinguishable. Comparison of theoretical estimates with a collection of the most recent experimental measurements shows reasonable agreement for the energetics of 4He and pure 3He. On the other hand, a significant discrepancy (already observed in previous studies) is reported between computed and measured values of the 3He kinetic energy in the mixture, especially in the limit of low 3He concentration. We assess quantitatively the importance of Fermi statistics and find it to be negligible for a 3He concentration ≲20%. Our results for the momentum distribution lend support to what was already hypothesized by other authors, namely, that the discrepancy is likely due to underestimation of the 3He kinetic energy contribution associated with the tail of the experimentally measured momentum distribution.

SACLAの高強度X線照射下の原子・分子の動的振舞い

We have investigated ultrafast electronic and nuclear dynamics in atoms, molecules and clusters induced by very intense（～50 μJ/μm2）, ultrashort（～10 fs） pulses generated by SACLA. At photon energy of 5.0～5.5 keV, we could identify that Xen+ with n up to 26 is produced, evidencing occurrence of deep inner-shell ionization and sequential electronic decay cycles repeated multiple times in the xenon atom within ～10 fs pulse duration. The results for momentum-resolved multiple ion coincidence study on iodine-contained organic molecules（iodomethane and 5-iodouracil）illustrates that the charges are produced by the cycles of deep inner-shell ionization of the iodine atom and sequential electronic decay and spread over the entire molecule within 10 fs, leading to Coulomb explosion. The measured momentum distributions and correlations are well reproduced by the model calculations. The results for electron spectroscopy on argon and xenon clusters, with help of model calculations, illustrate that nanoplasma is formed by the XFEL pulse in tens of fs, and continuous thermal emission from the plasma occurs in ps.

Large-momentum distribution of a polarized Fermi gas and p -wave contacts

We present a derivation of the adiabatic energy relations as well as the large momentum distribution of a polarized Fermi gas near p-wave Feshbach resonances. The leading asymptotic behavior ($k^{-2}$) and subleading behavior ($k^{-4}$) of the large momentum distribution have recently been predicted by Yu et al. [Phys. Rev. Lett. 115, 135304 (2015)] and by He et al. [Phys. Rev. Lett. 116, 045301 (2016)] using two different approaches. Here, we show that the subleading asymptotic behavior ($\sim k^{-4}$) can not fully be captured by the contact defined from the adiabatic energy relation related to the p-wave effective range, and there should be an extra term resulted from the center-of-mass motion of the pairs. The omission of this extra term is perhaps a reasonable approximation at zero temperature. However, it should be taken into account at finite temperature and should be of significant importance to understand the recently measured momentum distribution in a resonant p-wave Fermi gas of ultracold $^{40}$K atoms [Luciuk et al., Nature Phys. 12, 599 (2016)].

Experimental program of the Super-FRS Collaboration at FAIR and developments of related instrumentation

The physics program at the super-conducting fragment separator (Super-FRS) at FAIR, being operated in a multiple-stage, high-resolution spectrometer mode, is discussed. The Super-FRS will produce, separate and transport radioactive beams at high energies up to 1.5 AGeV, and it can be also used as a stand-alone experimental device together with ancillary detectors. Various combinations of the magnetic sections of the Super-FRS can be operated in dispersive, achromatic or dispersion-matched spectrometer ion-optical modes, which allow measurements of momentum distributions of secondary-reaction products with high resolution and precision. A number of unique experiments in atomic, nuclear and hadron physics are suggested with the Super-FRS as a stand-alone device, in particular searches for new isotopes, studies of hypernuclei, delta-resonances in exotic nuclei and spectroscopy of atoms characterized by bound mesons. Rare decay modes like multiple-proton or neutron emission and the nuclear tensor force observed in high-momentum regime can be also addressed. The in-flight radioactivity measurements as well as fusion, transfer and deep-inelastic reaction mechanisms with the slowed-down and energy-bunched fragment beams are proposed for the high-resolution and energy buncher modes at the Super-FRS.

Methods for detecting charge fractionalization and winding numbers in an interacting fermionic ladder

We consider a spin-1/2 fermionic ladder with spin–orbit coupling and a perpendicular magnetic field, which shares important similarities with topological superconducting wires. We fully characterize the symmetry-protected topological phase of this ladder through the identification of fractionalized edge modes and non-trivial spin winding numbers. We propose an experimental scheme to engineer such a ladder system with cold atoms in optical lattices, and we present two protocols that can be used to extract the topological signatures from density and momentum-distribution measurements. We then consider the presence of interactions and discuss the effects of a contact on-site repulsion on the topological phase. We find that such interactions could enhance the extension of the topological phase in certain parameters regimes.

Momentum-resolved study of the saturation intensity in multiple ionization

A momentum-resolved experimental study of strong-field multiple ionization of ionic targets is presented, and a method to deconvolve the measured momentum distributions and extract the saturation intensities is introduced.

The Quantum Mechanics of Nano-Confined Water: New Cooperative Effects Revealed with Neutron and X-Ray Compton Scattering

Neutron Compton scattering(NCS) measurements of the momentum distribution of light ions using the Vesuvio instrument at ISIS provide a sensitive local probe of the environment of those ions. NCS measurements of the proton momentum distribution in bulk water show only small deviations from the usual picture of water as a collection of molecules, with the protons covalently bonded to an oxygen and interacting weakly, primarily electrostatically, with nearby molecules. However, a series of measurements of the proton momentum distribution in carbon nanotubes, xerogel, and Nafion show that the proton delocalizes over distances of 0.2-0.3Å when water is confined on the scale of 20Å. This delocalization must be the result of changes in the Born-Oppenheimer surface for the protons, which would imply that there are large deviations in the electron distribution from that of a collection of weakly interacting molecules. This has been observed at Spring-8 using x-ray Compton scattering. The observed deviation in the valence electron momentum distribution from that of bulk water is more than an order of magnitude larger than the change observed in bulk water as the water is heated from just above melting to just below boiling. We conclude that the protons and electrons in nano-confined water are in a qualitatively different ground state from that of bulk water. Since the properties of this state persist at room temperature, and the confinement distance necessary to observe it is comparable to the distance between the elements of biological cells, this state presumably plays a role in the functioning of those cells.

Recovering the Fermi surface with 2D-ACAR spectroscopy in samples with defects

When two-dimensional angular correlation of positron annihilation radiation (2D-ACAR) experiments are performed in metals containing defects, conventional analysis in which the measured momentum distribution is folded back into the first Brillouin zone is rendered ineffective due to the contribution from positrons annihilating from the defect. However, by working with the radial anisotropy of the spectrum, it is shown that an image of the Fermi surface can be recovered since the defect contribution is essentially isotropic.

Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

We describe the use of the exact Yang-Yang solutions for the one-dimensional Bose gas to enable accurate kinetic-energy thermometry based on the root-mean-square width of an experimentally measured momentum distribution. Furthermore, we use the stochastic projected Gross-Pitaevskii theory to provide a quantitative description of the full momentum distribution measurements of Van Amerongen et al. [Phys. Rev. Lett. 100, 090402 (2008)]. We find the fitted temperatures from the stochastic projected Gross-Pitaevskii approach are in excellent agreement with those determined by Yang-Yang kinetic-energy thermometry.

Nonlinear Fourier-transform spectroscopy ofD2using high-order harmonic radiation

High-order harmonic radiation is available to investigate ultrafast nonlinear optical phenomena, such as two-photon absorption process, in the vacuum and extreme ultraviolet wavelength region. We have determined the sequential two-photon dissociative ionization pathways of D2 with the simultaneous irradiation of multiple order harmonics of a Ti:sapphire laser in the visible-vacuum ultraviolet region with the aid of both an interferometric autocorrelation measurement and a Fourier-transform spectroscopy. By analyzing the interferometric autocorrelation signals appearing in the measured momentum distribution of D + , we were able to decompose the measured momentum distribution into three momentum distribution images representing the three distinct dissociation pathways, which are sequentially two-photon excitation processes of D2. \({\mathrm{D}}_{2}^{+}\) is prepared in the electronic ground state of \({\mathrm{D}}_{2}^{+}\), and then excited to the first excited state, leading to the dissociation into D + and D.