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DOE OSTI2020

Emergence of p+ip superconductivity in two-dimensional doped Dirac systems

Searching for the $p + ip$ superconducting (SC) state has become a fascinating subject in condensed matter physics recently, as a dream application awaiting in topological quantum computation. Unfortunately, so far there is no universal principle for realizing $p + ip$ in generic solid-state systems. Here we report a theoretical discovery of a $p + ip$ SC ground state (coexisting with ferromagnetic order) in the honeycomb lattice Hubbard model in the extremely strong-coupling limit (e.g., infinite U) at low doping $(δ < 0.2)$, by using both the state-of-art Grassmann tensor product state approach and a continuum quantum field theory approach. Our discovery suggests a mechanism for the $p + ip$ SC state in generic strongly correlated systems based on spin-charge separation and the charge current–current coupling scenario, which opens a door towards experimental realization. The $p + ip$ SC state has an instability towards a potential non-Fermi liquid with a large but finite U . Nevertheless, by applying an in-plane Zeeman field, such a $p + ip$ SC state can be stabilized with finite U in a very wide range of doping. Relevant realistic materials are also proposed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Hadronic resonance production and interaction in p-Pb collisions at LHC energies in EPOS3

Using the EPOS3 model with the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model to describe the hadronic phase, we study the production of short-lived hadronic resonances and the modification of their yields and p T spectra in p-Pb collisions at √sNN= 5.02 TeV. High-multiplicity p-Pb collisions exhibit similar behavior to midperipheral Pb-Pb collisions at LHC energies, and we find indications of a short-lived hadronic phase in p-Pb collisions that can modify resonance yields and p T spectra through scattering processes. The evolution of resonance production is investigated as a function of the system size, which is related to the lifetime of the hadronic phase in order to study the onset and evolution of scattering effects in p-Pb collisions. We also study hadron production separately in the core and corona parts of these collisions and explore how this division affects the total particle yields as the system size increases.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Importance of initial and final state effects for azimuthal correlations in p + Pb collisions

In this work, we investigate the relative importance of initial and final state effects on azimuthal correlations of gluons in low and high multiplicity p+Pb collisions. To achieve this, we couple Yang-Mills dynamics of pre-equilibrium gluon fields (IP-GLASMA) to a perturbative QCD based parton cascade for the final state evolution (BAMPS) on an event-by-event basis. We find that signatures of both the initial state correlations and final state interactions are seen in azimuthal correlation observables, such as v 2 {2PC} (p T ), their strength depending on the event multiplicity and transverse momentum. Initial state correlations dominate v 2 {2PC} (p T ) in low multiplicity events for transverse momenta p T > 2 GeV. Lastly, while final state interactions are dominant in high multiplicity events, initial state correlations affect v 2 {2PC} (p T ) for p T > 2 GeV as well as the pT integrated v 2 {2PC}.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Nonlinear dynamics and quantum chaos of a family of kicked p -spin models

Herein we introduce kicked p-spin models describing a family of transverse Ising-like models for an ensemble of spin-1/2 particles with all-to-all p-body interaction terms occurring periodically in time as delta-kicks. This is the natural generalization of the well-studied quantum kicked top (p = 2) [Haake, Kus', and Scharf, Z. Phys. B 65, 381 (1987)]. We fully characterize the classical nonlinear dynamics of these models, including the transition to global Hamiltonian chaos. The classical analysis allows us to build a classification for this family of models, distinguishing between p = 2 and p > 2, and between models with odd and even p's. Quantum chaos in these models is characterized in both kinematic and dynamic signatures. For the latter, we show numerically that the growth rate of the out-of-time-order correlator is dictated by the classical Lyapunov exponent. Finally, we argue that the classification of these models constructed in the classical system applies to the quantum system as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Physical properties of intergrowth compound Eu 2 CuZn 2 P 3

Here, the physical properties of single-crystalline Eu 2 ⁢CuZn 2 ⁢P 3 were inspected via thermodynamic, transport, and neutron diffraction measurements. Eu 2 ⁢ CuZn 2⁢ P 3 is composed of EuCuP and EuZn 2 ⁢ P 2 motifs stacked in a one-to-one ratio. The magnetic response of Eu 2 ⁢ CuZn 2 ⁢ P 3 is similar to that of EuZn 2 ⁢ P 2 in its A-type antiferromagnetic (semiconducting) state. A Néel temperature of T N = 40.3K is obtained from the specific heat capacity. Single-crystal neutron diffraction reveals a (001) magnetic propagation vector, with primarily in-plane moments coupled along [001] in an up-up-down-down pattern. This spin structure retains the ferromagnetic EuCuP motifs and antiferromagnetic coupling across the EuZn 2 ⁢P 2 motifs. The electrical resistivity is characterized by metallic behavior above 100 K, an increase in ρ upon cooling below ≈ 75K, and a large negative magnetoresistance below T N . First principles calculations evidence a narrow band gap for antiferromagnetic ordering and semimetallic behavior for the ferromagnetic state. This is consistent with the observed effect of magnetic field on the electrical resistivity. Hall effect measurements reveal a field-induced, negative anomalous Hall effect that increases on cooling down to 2 K. Also, an unconventional contribution to the Hall effect dominates the low-field Hall signal, particularly near T N , and is similar in appearance to a topological Hall effect. However, further work is necessary to understand if any of the transport properties have topological origins or if magnetism-induced modifications to the Fermi surface induce these unusual Hall effect signals in this and related materials.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Magnetoelastic-coupling-assisted first-order antiferromagnetic transitions in the corrugated honeycomb-lattice compounds (Ca, Sr) ⁢Mn 2 ⁢ P 2

Understanding the origin of unconventional magnetic order is a central theme in the research field of functional quantum materials for spin-dependent applications. In general, a paramagnetic (PM) to antiferromagnetic (AFM) transition is of thermodynamically second order in nature in the absence of a magnetic field. In the magnetically frustrated corrugated-honeycomb lattice compounds (Ca, Sr) ⁢Mn 2 ⁢ P 2 , electrical resistivity 𝜌 measurements in the 𝑎⁢𝑏 plane are reported to exhibit sharp discontinuities at the respective PM to AFM ordering temperatures 𝑇 N = 69.5 and 53 K, respectively, signifying the unusual first-order nature of the AFM transition. To reveal the origin of such anomalous transitions, high-resolution linear thermal-expansion measurements are reported for both CaMn 2 ⁢P 2 and SrMn 2 ⁢ P 2 in the 𝑎⁢𝑏 plane and along the 𝑐 axis using capacitance dilatometry. The thermal expansion measurements show a sharp discontinuity in Δ⁢𝐿/𝐿 at 𝑇 N , yielding a diverging behavior in the thermal expansion coefficient 𝛼⁡(𝑇) associated with strong magnetoelastic coupling, driving the first-order AFM transition in CaMn 2 ⁢P 2 . However, this effect is weaker in SrMn 2 ⁢P 2 , consistent with the magnetic entropy changes 𝑆⁡(𝑇) obtained from the heat-capacity measurements. Temperature-dependent 𝑎⁢𝑏-plane x-ray diffraction measurements for CaMn 2 ⁢ P 2 near its 𝑇 N yield a volume thermal expansion coefficient consistent with literature data for other materials. The uniaxial pressure derivatives of 𝑇 N in the two compounds are found to be respectively opposite in sign, presumably due to the different magnetic structures.

Pakhira, Santanu [Maulana Azad National Institute ↗

DOE OSTI2015

SU-E-P-09: Compliance With Evidence-Based Treatment Planning DVH Guidelines In An Academic Multi-Site Radiation Oncology Practice Setting

Purpose: To evaluate the compliance with evidence-based treatment planning organ-at-risk (OAR) guidelines in a single institution with four practice sites. Methods: Two hundred thirteen head and neck cancer patients treated between September 2009 and September 2013 were retrospectively selected. Consensus treatment planning guidelines, including OAR dose constraints, were established based on institutional experience and published data. Data spanned a time period of 2 years prior to (n=112) and 2 years post-enactment (n=101) of the guidelines. We investigated the differences in the frequency with which (1) OARs were contoured and (2) OAR DVH goals were met. Trends in the proportion with OAR contours over time was tested using linear regression. Trends in the proportion of contoured OARs achieving clinical DVH goals were similarly tested. The proportion of patients contoured and meeting DVH goals before and after guidelines was compared using a test of proportions. Results: When the proportion of cases with OAR contours before and after guidelines were compared, we observed an increase from 75% to 87% (p=0.02) for the brainstem, decrease from 97% to 88% (p=0.01) for the cord and increase from 47% to 77% (p<0.001) for the mandible. For the proportion of cases with OAR contours in which clinical goals were met, a significant decrease from 99% to 90% was observed for the cord V48<0.3% (p=0.001). A significant decrease in the proportion of cases with left parotid contours (from 92% to 73% (p=0.03)) was observed over 2 years after guideline enactment and the proportion meeting the clinical DVH goal of V30<50% increased significantly from 36% to 50% (p=0.007) over the 2 years after guidelines. Conclusion: The enactment of OAR planning guidelines resulted in an increase in OAR contour compliance, overall. In cases with OAR contours, there was little to no change in the proportion that met clinical goals.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

SU-E-P-55: The Reaserch of Cervical Cancer Delivered with Constant Dose Rate and Gantry Speed Arc Therapy(CDR-CAS-IMAT) On Conventional Linac

Purpose: Postoperative cervical cancer patients with large target volume and the target shape is concave, treatmented with static intensity-modulated radiotherapy (IMRT) is time consuming. The purpose of this study is to investigate using constant dose rate and gantry speed arc therapy(CDR-CAS-IMAT) on conventional linear accelrator, by comparing with the IMRT technology to evaluate the performance of CDR-CAS-IMAT on postoperative cervical cancer patients. Methods: 18 cervical cancer patients treated with IMRT on Varian 23IX were replanted using CDR-CAS-IMAT. The plans were generated on Oncentra v4.1 planning system, PTV was prescribed to 50.4 Gy in 28 fractions. Plans were evaluated based on the ability to meet the dose volume histogram. The homogeneity index (HI), conformity index (CI) of target volume, the dose of organs at risk, radiation delivery time and monitor units were also compared. SPSS 19.0 software paired T-test analysis was carried out on the two sets of data. Results: Compared with the IMRT plans PTV’s CI (t= 3.85, P =0.001), CTV’s CI, HI, D90, D95, D98, V95, V98, V100 (t=4.21, −3.18, 2.13, 4.65, 7.79, 2.29, 6.00, 2.13, p=0.001, 0.005, 0.049, 0.000, 0.000, 0.035, 0.000, 0.049), and cord D2 and rectum V40 (t=−2.65, −2.47, p= P =0.017, 0.025), and treatment time and MU (t=−36.0, −6.26, P =0.000, 0.000) were better than that of IMRT group. But the IMRT plans in terms of decreasing bladder V50, bowel V30 (t=2.14, 3.00, P =0.048, 0.008) and low dose irradiation volume were superior to that of CDR-CAS-IMAT plans. There were no significant differences in other statistical index. Conclusion: Cervical cancer patients with CDR-CAS-IMAT on Varian Clinical 23IX can get equivalent or superior dose distribution compared with the IMRT technology. IMAT have much less treatment time and MU can reduce the uncertainty factor and patient discomfort in treatment. This work was supported by the Medical Science Foundation of the health department of Hebei Province (No. 20130253)

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

SU-F-P-27: The Study of Actual DVH for Target and OARs During the Radiotherapy of Non-Small Cell Lung Cancer

Purpose: To analyze the changes of the volume and dosimetry of target and organs at risk (OARs) by comparing the daily CBCT images and planning CT images of the patients with Non-Small Cell Lung Cancer (NSCLC) and analyze the difference between planned dose and accumulated dose. Methods: This study retrospectively analyzed eight cases of non-small cell lung cancer patients who accepted CRT or IMRT treatment and KV-CBCT. For each patient, the prescription dose was 60Gy and the fraction dose was 2Gy. Deform the daily CBCT images to planning CT images by the mapping of registration to compare the planning dose with cumulative dose of targets and organs at risk in RayStation. Results: The average volume of GTV of 8 patients with CBCT was 88.26% of the original volume. The average plan dose of GTV was 64.49±2.40Gy. The accumulated dose of GTV was 60.13±2.70Gy (P≤0.05). The average volume of PTV to reach the prescription dose was 95.59% for original plan and 81.47% for accumulated plan (P≤0.05). The volume changes of the left and right lung of the original volume was 88.95% and 80.32%, respectively. The average dose of the left and right lung of original plan was 9.31±1.75Gy and 4.33±1.10Gy, respectively(P≥0.05). The average accumulated dose was 9.63±1.96Gy and 4.63±1.36Gy, respectively(P≥0.05). The average plan dose and accumulated dose of heart was 6.88±1.70Gy and 6.38±0.91Gy, respectively (P≥0.05). The average plan maximum dose and accumulated dose for spinal cord was 24.62±5.91Gy and 26.00±5.14Gy, respectively (P≥0.05). Conclusion: The changes of target anatomical structure with NSCLC make difference between the planned dose and cumulative dose. With the dose deformation method, the dose gap can be found between planning dose and delivery dose.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

Ceramics Based on Powder Mixtures Containing Calcium Hydrogen Phosphates and Sodium Salts (Na{sub 2}CO{sub 3}, Na{sub 4}P{sub 2}O{sub 7}, and NaPO{sub 3})

Ceramic materials in the Na{sub 2}O–CaO–P{sub 2}O{sub 5} system have been produced using powder mixtures containing calcium hydrogen phosphates (monetite/brushite: CaHPO{sub 4}/CaHPO{sub 4} ∙ 2H{sub 2}O) and sodium salts (Na{sub 2}CO{sub 3} ∙ H{sub 2}O, Na{sub 4}P{sub 2}O{sub 7} ∙ 10H,O, and NaPO{sub 3}). These salts were used as precursors to the following high-temperature phases: Сa{sub 2}P{sub 2}O{sub 7}, Na{sub 2}O, Na{sub 4}P{sub 2}O{sub 7}, and NaPO{sub 3}. The amount of the salts in the powder mixtures was such that the oxide composition of the ceramics corresponded to 10 mol % sodium oxide for each mixture in the Na{sub 2}O–CaO–P{sub 2}O{sub 5} system. The powder mixtures were prepared using mechanical activation in acetone, which was accompanied by monetite rehydration to brushite. X-ray diffraction characterization showed that, after firing, the phase composition of the ceramics produced from the powder mixtures thus prepared lay in the Сa{sub 2}P{sub 2}O{sub 7}–NaCaPO{sub 4}–Na{sub 2}СaP{sub 2}O{sub 7}–Са(РО{sub 3}){sub 2} phase field. The resultant ceramic materials contain biocompatible and bioresorbable phases and can be recommended for bone implant fabrication.

36 MATERIALS SCIENCE↗

DOE OSTI2013

Spectral temperatures of {Delta}{sup 0}(1232) resonances produced in p{sup 12}C and d{sup 12}C collisions at 4.2 GeV/c per nucleon

The reconstructed experimental transverse momentum (p{sub t}) distributions of {Delta}{sup 0}(1232) resonances produced in p{sup 12}C and d{sup 12}C collisions at 4.2 A GeV/c and the corresponding spectra calculated using Modified FRITIOF model were analyzed in the framework of Hagedorn Thermodynamic Model. The spectral temperatures of {Delta}{sup 0}(1232) resonances were extracted from fitting their p{sub t} spectra with one-temperature Hagedorn function. The extracted spectral temperatures of {Delta}{sup 0}(1232) were compared with the corresponding temperatures of {pi}{sup -} mesons in p{sup 12}C and d{sup 12}C collisions at 4.2 A GeV/c obtained similarly from fitting the p{sub t} spectra of {pi}{sup -} by one-temperature Hagedorn function. The spectral temperatures of {Delta}{sup 0}(1232) resonances agreed within uncertainties with the corresponding temperatures of {pi}{sup -} mesons produced in p{sup 12}C and d{sup 12}C collisions at 4.2 A GeV/c.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Effect of Dislocation-related Deep Levels in Heteroepitaxial InGaAs/GaAs and GaAsSb/GaAs p–i–n Structures on the Relaxation time of Nonequilibrium Carriers

The results of an experimental study of the capacitance–voltage (C–V) characteristics and deep-level transient spectroscopy (DLTS) spectra of p{sup +}–p{sup 0}–i–n{sup 0} homostructures based on undoped dislocationfree GaAs layers and InGaAs/GaAs and GaAsSb/GaAs heterostructures with homogeneous networks of misfit dislocations, all grown by liquid-phase epitaxy (LPE), are presented. Deep-level acceptor defects identified as HL2 and HL5 are found in the epitaxial p{sup 0} and n{sup 0} layers of the GaAs-based structure. The electron and hole dislocation-related deep levels, designated as, respectively, ED1 and HD3, are detected in InGaAs/GaAs and GaAsSb/GaAs heterostructures. The following hole trap parameters: thermal activation energies (E{sub t}), capture cross sections (σ{sub p}), and concentrations (N{sub t}) are calculated from the Arrhenius dependences to be E{sub t} = 845 meV, σ{sub p} = 1.33 × 10{sup –12} cm{sup 2}, N{sub t} = 3.80 × 10{sup 14} cm{sup –3} for InGaAs/GaAs and E{sub t} = 848 meV, σ{sub p} = 2.73 × 10{sup –12} cm{sup 2}, N{sub t} = 2.40 × 10{sup 14} cm{sup –3} for GaAsSb/GaAs heterostructures. The concentration relaxation times of nonequilibrium carriers are estimated for the case in which dislocation-related deep acceptor traps are involved in this process. These are 2 × 10{sup –10} s and 1.5 × 10{sup –10} s for, respectively, the InGaAs/GaAs and GaAsSb/GaAs heterostructures and 1.6 × 10{sup –6} s for the GaAs homostructures.

36 MATERIALS SCIENCE↗

DOE OSTI2017

The Numerical Simulation of the Nanosecond Switching of a p-SOS Diode

Abrupt high-density reverse current interruption has been numerically simulated for switching from forward to reverse bias in a silicon p{sup +}P{sub 0}n{sup +} structure (p-SOS diode). It has been shown that the current interruption in this structure occurs as a result of the formation of two dynamic domains of a strong electric field in regions in which the free carrier concentration substantially exceeds the concentration of the doping impurity. The first domain is formed in the n{sup +} region at the n{sup +}P{sup 0} junction, while the second domain is formed in the P{sup 0} region at the interface with the p{sup +} layer. The second domain expands much faster, and this domain mainly determines the current interruption rate. Good agreement is achieved between the simulation results and the experimental data when the actual electric circuit determining the electron–hole plasma pumping in and out is accurately taken into account.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Iron isotope fractionation between solid and liquid metal in the Fe-P±Ni system: Experimental constraints and implications for meteorites

Iron meteorites record a range of Fe isotope compositions that hold valuable information regarding the evolution of their parent bodies. Interpreting this isotopic variability, however, requires experimental constraints on the equilibrium isotope fractionation between phases. It is thought that the cores of many iron meteorite parent bodies experienced fractional crystallization, during which crystallization of solid iron-nickel occurs from an increasingly non-metal-rich liquid alloy. Phosphorus is one component of this alloy, and this study provides the first constraints on Fe-isotope fractionation between solid and liquid alloys in the Fe-Ni-P system. Experiments comprising Fe and P show a clear enrichment in the light isotopes of Fe in the liquid phase, which increases with the amount of phosphorus. Nickel-bearing samples are offset from the trend defined by Ni-free experiments, which is accounted for by the change in the solid alloy phase from a body-centered cubic to face-centered cubic structure upon the addition of Ni. The increasing light isotope enrichment of the liquid with increasing P content suggests interstitial solution of P, which is known to lengthen Fe-Fe bonds in Fe-P liquids (Waseda and Shiraishi 1977). Results suggest a negligible effect of P on Fe isotope fractionation during planetesimal core crystallization. Iron isotopes may, however, prove useful for identifying the petrogenesis of schreibersite in pallasites and iron meteorites.

58 GEOSCIENCES↗

DOE OSTI2023

The high energy X-ray probe (HEX-P): Galactic PeVatrons, star clusters, superbubbles, microquasar jets, and gamma-ray binaries

HEX-P is a probe-class mission concept that will combine high spatial resolution X-ray imaging (<10" FWHM) and broad spectral coverage (0.2–80 keV) with an effective area far superior to current facilities (including XMM-Newton and NuSTAR) to enable revolutionary new insights into a variety of important astrophysical problems. With the recent discoveries of over 40 ultra-high-energy gamma-ray sources (detected above 100 TeV) and neutrino emission in the Galactic Plane, we have entered a new era of multi-messenger astrophysics facing the exciting reality of Galactic PeVatrons. In the next decade, as more Galactic PeVatrons and TeV gamma-ray sources are expected to be discovered, the identification of their acceleration and emission mechanisms will be the most pressing issue in both particle and high-energy astrophysics. In this paper, along with its companion papers, we will present that HEX-P is uniquely suited to address important problems in various cosmic-ray accelerators, including Galactic PeVatrons, through investigating synchrotron X-ray emission of TeV–PeV electrons produced by both leptonic and hadronic processes. For Galactic PeVatron candidates and other TeV gamma-ray sources, HEX-P can fill in a large gap in the spectral-energy distributions (SEDs) of many objects observed in radio, soft X-rays, and gamma rays, constraining the maximum energies to which electrons can be accelerated, with implications for the nature of the Galactic PeVatrons and their contributions to the spectrum of Galactic cosmic rays beyond the knee at ~3 PeV. In particular, X-ray observation with HEX-P and TeV observation with CTAO will provide the most powerful multi-messenger diagnostics to identify Galactic PeVatrons and explore a variety of astrophysical shock mechanisms. We present simulations of each class of Galactic TeV–PeV sources, demonstrating the power of both the imaging and spectral capabilities of HEX-P to advance our knowledge of Galactic cosmic-ray accelerators. In addition, we discuss HEX-P’s unique and complementary roles to upcoming gamma-ray and neutrino observatories in the 2030s.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

The high energy X-ray probe (HEX-P): Galactic PeVatrons, star clusters, superbubbles, microquasar jets, and gamma-ray binaries

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1990

Small gain robustness issues in the p-integrator repetitive controller

The basic theory of the digital p-integrator controller is utilized to modify the command to a stable analog feedback control system in order to produce zero tracking error of a repetitive command. Mapping of continuous time poles and zeros to the images in the discrete time domain is performed. It is shown that for a pole excess of one, with p odd, the p-integrator learning controller will often produce a stable learning process, even for relatively large sample times. For a pole excess of two, a stable learning process can often be achieved for any p as long as the sample time is kept sufficiently short. Therefore, when the pole excess is zero and one utilizes the proper p-integrator controller with p odd, stable performance is often produced, even for relatively large sample times.

Longman, Richard W.↗

NASA NTRS1994

Effect of nonlinear interactions on p-mode frequencies and line widths

We calculate the effect of nonlinear interactions among solar acoustic modes upon the modal frequencies and energy loss rates (or line widths). The frequency shift for a radial p-mode of frequency 3 mHz is found to be about -0.5 microHz. The magnitude of nonlinear frequency shift increases more rapidly with frequency than the inverse mode mass (mode mass is defined as the ratio of energy in the mode to its surface velocity amplitude squared). This frequency shift is primarily due to nonresonant three-mode interactions and is dominated by high l surface gravity waves (f-modes) and p-modes. The line width of a radial p-mode of frequency 3 mHz, due to resonant nonlinear interactions, is about 0.3 microHz. This result is consistent with that of Kumar and Goldreich (1989). We also find, in agreement with these authors, that the most important nonlinear interactions of trapped p-modes involve f-modes and high-frequency p-modes (frequency greater than about 5 mHz) which propagate in the solar photosphere. Thus, using the arguments advanced by Kumar & Goldreich (1989), we conclude that nonlinear couplings cannot saturate the overstable solar p-modes at their small observed amplitudes. Both the nonlinear frequency shifts and line widths, at a fixed frequency, are proportional to the inverse of mode mass which for modes of degree greater than about 100 is approximately l(exp 0.8). Therefore, the frequency of an f-mode of l = 1000, due to nonlinear interactions, is decreased by approximately 0.4%.

Kumar, Pawan↗